All students will act as the teacher. Each of you will comment on the strategy
that you will use to teach someone about differentiation of polynomials, logs and ln.
All the common errors you have observed can now be avoided, how?
What is your strategy in your teaching to avoid these errors?
90 comments:
Hum teacher,well firstly you ought to now the background and foundation of your students in order to approach them.Start with the basics and rules, keep it simple!Then introduce the simple questions, give assignments and a surprise quiz on the very next class.Now you do the assessment and stress on the mistakes observed.Now after this is achieved you can take the risk of inviting the more difficult questions and doing the same assessment.P.S> the assessments are not long ones so its not time consuming.
Arirosa
What you said is fine. But what I am asking is quite different.
You have been reading comments and have been discovering common errors. You are concluding the topic.
What stategies will be give to assist these students to prevent them from making the same errors?
TO ANYONE:
I having a little problem in understanding exactly what this blog want me to explain. Could you please make it a little easier for me to understand. It will also make things a little clearer for future users on this blog.
Thank You.
alright given this example(which i did wrong)
y = 2/3x^4
if u examine this problem closely u see that it is the same as
y = 2/3 multiply by 1/x^4
also remembering that 1/x^4 is the same as x^-4
so we further get 2/3 multiply by x^-4
and this is the case with all fractions so you should make a mental note of this
eh captain vegie jus imagine you is d teacher
and explain as simply as you could the common errors in solving problems in logs or any other subject
P.S. (i real like yuh user name dog lollollollol)
so in continuation if u are asked to differentiate let us say
y = 4/5x^4
jus simply rearrange to
y = 4/5 (x^-4)
dy/dx =
-4 x 4/5 (x^-4-1)
which is
-16/5(x^-5)
voila
TO: SIR MOOSE
Thank you for taking the time to explain the question to me. I will now contemplate upon the errors that I would usually make.
There are several errors that can be made in differentition. I will se if i could hilight some of these:
1. lets take the common
y= 5/2x^3
it would be very tempting to do the following:
y= 5(2x^-3)
This is very wrong
The correct notation would be:
y= 5/2(x^-3)
REMEMBER: y= 5/2x^3 is the same as writing the following:
y = 5/2(x^-3)
Another common error:
When x is differentiated the answer is 1. This may seem trivial but in the haste during an exam this very important detail can be overlooked. REMEMBER X is 1x^1.
Probably what is most of all important to look out for in differentiation and most simple to make errors in is know what you are differentiating.
I mean if the ask you to differentiate pressure with respect temperature. The notation would be dp/dt not dy/dx or any other combination of the alphabet.
Remember:
SIGNS one of the most easy error to make in differentiation. Take into careful consideration the policeman. He will always be watching for you to make and error with your negative signs.
eg. y= -3x^-2
The solution would be:
dy/dx= +6x^-3
It can also come with a two for one special, I mean:
y = -3/x^2
REMEMBER this qusetion has two major errors that you can make so be careful.
A wise lecturer once told me when in dbout use your calculator. If you know your directed numbers are on unstable grounds use your calculator. This comes into play when subtracting one from the power when differentiating. Your directed numbers may not be on unstable grounds but again it is very easy to make an error such as:
-3-1= -2
REMEMBER: The policeman is always watching.
LOGS:
And first place in the logs error awards goes to:
log(3x+2) = log 3x + log 2
I made this mistake so much times it would seem that i invented the error. Don't make this error.Learn from my errors. log(3x+2) is one term and should be treated as such. REMEMBER at this level of questioning sometimes the obvious is a clear indication that we are doing something wrong. Be ever watchful.
Just to re-enforce my last comment lets take an example:
log(3x+2) where x= 5
it would simplify to: log(17)
Agree?
Now what the error would make us do is the following:
log 3x + log 2
log 15 + log 2
The former is definitely not the same as the latter. Do we agree?
fancy a go at this one:
y= log[5] (x^4-9x^-2+x+3.25)
Find dy/dx
There are several errors that can be made in this question. Please excuse the format of the syntax the computer does not allow it any other way. REMEMBER your base of the log.
I feel that when someone is making a lot of errors it can be because they are not confident in their answers. So my approach is to a simple question to build confidence then attempt back the harder question. Is this of any help to anyone?
y=log [5](x^4-9x^-2+x+3.25)
u = x^4 - 9x^-2 + x + 3.25
du/dx = 4x^3 + 18^-3 + 1
dy/dx = (1/u)* (du/dx)*(log[5] e)= (1/{x^4-9x^-2+x+3.25})*(4x^3+18^-3+1)*log[5]e
continuing my previous comment
to work this question you should first state what you are working with.
state you y, u and the derivative of u. this way oyou will know exactly what you have to work with.
state the formula that needs to be used and then substitute
continuing the same comment:
remember to pace yourself and carfully transfer the values you calculated previously into you equation
Hellion:
Also be sure to paty attention to any "policemen" encountered. i.e. any minus signs. be sure to take it slow when approaching a minus sign.
tvthank you peebles that is a good point.alway remebr you basic and simplest rules because these are where the most mistakes are made
wel if i were to explain someting to someone i would use simple every day examples relating to the topic...examples use words such as marbles, money , oranges , balls etc..this may avoid errors as the person you are trying to explain to may understand wat u are tring to explain..
moose
From your first comment,
your stratehy to avoid errors like that in future is -
A term with a fraction should be separated as a number (fraction) part and as a variable part.
suppose I am having problems with my basic rules in logarithms or I can't tell when to use it, how can can u help me in understanding and doing logs.
Hellion:
when u found the first diffrential of your question:
u got: du/dx = 4x^3 + 18^-3 + 1
I believe that the last term (1) was suppose to be left out. NOT SO? because the diffential of 3.25 is suppose to be nothing becuase there is no x in front of the term 3.25
Captain vegetable
I do think your awrd for log errors is quite correct.
This is due to working in a hurry.
What i like do in particular is get the attention of the students!
i will have to "read" them to see what they like to hear! on doing this i would teach what ever i am doing in relation to what it is they like! in doing this i would have there attention and if i say something out of the way they would be able to pick up on it!
pebbles:
there is a x term before 3.25 in captain vegetables original comment.
Yoshi:
Logs is based soley on exponents which is powers. When ever a question is not possible in all ways, logs is a way of solving such questions. So u use logs whenever powers are involved
Hellion.
Nope there is no x
y= log[5] (x^4-9x^-2+x+3.25)
This is the exact question. its:
x to the power of 4 minus nine x to the power of minus two plus x plus 3.25
Hellion thats a simple mistake u are about to make. Slow down and do not rush the question
Firstly you have to outline all the errors that were made by the student or students.Using simple examples to highlight what was there mistake.Afterwards give him/her questions to make corrections to, using the the same error that were made by them, so as to see if they are understands what they are doing.
yes Pebbles! i see what you are speaking about! what Hellion did was that it was really x^1 which is really 1x^1 = 1x1 and don't forget to decrease the power if x by 1 which will be x^0 which is 1 so then every thing together will be 1x1x1 which is 1
i would ask questions based upon the topics so that i would get an idea of how my students think and the knowledge the they have based on the topics and help them to apply the knowledge they have to work out the questions.If they dont have much knowledge based on the topic i would try to teach them in a way where they get involoved,like asking my students to come up on the board and work the questions that they dont understand and correcting them where they may make errors,so as they go along they can learn in many different ways by hearing the work being taught and by doing the questions on the board there will learn by writting.
well, to discover the faults in the accuracy of solving the questions, it is obvious that some students would feel embarrased to ask for assistance because he or she didnt get the answer. so therefore i give a small assignment, nothing too big, on each principle of differentiation and logs and ask whoever understands and whoever looks shaky and not confident in there answer, i would ask them to work the answer. also a surprise quiz , not really worth any marks, every once in a while would keep them on there toes.
i tink the best strategy in helping someone learn logs or differentiation, is to take About half hour to teach piece of the topic ,,, because i tink after continuous talking ... students minds get saturated an they get distracted easily... therefore after half our of teaching.... questions should be given in class and worked step by step ensuring they understND it ... then get them to respond... then give home work ...
To Sparkle:
Lets say that you are teaching someone differentiation of polynomials who has never done that topic. What is the first thing that you would introduce to that student?
A student can know all there is to know about the various types of errors present in a particular topic. But sometimes in the haste of an exam these errors are still made by the student.
How can we avoid this?
There are multiple ways in dealing with this. Firstly a student must be able to perform his/her best under exam conditions. From my experience exam conditions can cause a student to make very trivial errors at the expense of the student's marks. A good practice for this is: Each time you get an assignment allot a suitable time limit in order to complete the assignment. By doing this it simulates exam conditions and the mental strains associated with it. REMEMBER: You may know the work but if you can't properly put it down on paper during an exam your marks will be on the line.
Another point: Knowing the error is all well and good. A student can have a well defragmented data bank of errors....
ACTUALLY identifying the errors, in a real question, that is another chapter.
From my experience in exams errors are themselves 'disguised'. So that when you think you are in the clear check again or you might regret it.
lets take an example:
y = -4/x^3 (find dy/dx)
First thing to note, they are testing to see what i would do with with the denominator.
But look just waiting in the 'shadows of error' is the ever vigilant policeman. The point I am trying to make is most of the times they would test more than one concept from a single qusetion. What would the answer to the question be?
the first thing i would teach a student who is now learning differentiation is to teach them the basic differenial rrules i.e.
y = an^x
dy/ dn = xan^x-1
To Everyone:
In an exam avoiding the errors in the first place is the first line of defence in not getting the question wrong. However let's assume that the error has been made. How can we recognise that we have made an error? Please share your thoughts.
REMEMBER: In your response you must bear in mind that time in an exam is as good as gold.....so to speak.
To Apocalypse:
It was found that the best way to re-enforce a concept that you have learnt is to correctly teach it to someone else. Bearing this in mind permit me to be your student.
SIR: My first question is: Who is dy/dn? Where he come from?
SRY FOR D LONG EXPLANATION. CAPTAIN VEGI ASK 4 IT!!! OH AND IS 4 YOUR OWN GUD!!!!!!
If u don’t understand differentiation please read. U wud understand beta if had a paper and a pen. Please get a paper and a pen.
For those of u who still don’t kno how to differentiate a polynomial, its very simple. They can bring function or terms in 3 main forms for u to differentiate
Consider the 1st form y = ax^n. dy/dx can be found by multiplying the power by the coefficient, then minus 1 from the power. For example if y = 3x^6 then dy/dx wud be 18x^5. Understand.
Now wat if u had to differentiate “x” this is no different from the first form. U kno that 1 is understood as the power and the coefficient right. Is x the same ting as 1x^1??? Of course it is!!!! Using the same method of differentiation I showed u above find dy/dx of 1x^1. u wud get 1x^0. True? Remember anything to the power 0 is 1, so ur answer is 1 now u try to differentiate 4x. Wat wud u get?? U got 4 right??? U did didn’t u??? I hope so. Now if u notice sumting, wen we differentiating anyting of the form “ax” we will always end up with “a” Once u are differentiating anyting of the form ‘ax” the differential is always “a” ok?????
Lets get into sum real stuff now. Wat if u had to differentiate sumting like 4/x^5, how wud u go about finding dy/dx. Wat u tink is the best ting to do from here??? Anytime u have to differentiate a function of that form, bring it to a polynomial. U kno… like ax^n
If we bring 4/x^5 to a polynomial we wud get 4x^-5. Note that the sign on the power change in going from the denominator to the numerator. That jus sumting u have to remember. As u can c this is of the form ax^n. now u can differentiate as I showed u above. Wat wud u get if u differentiate 4x^-5. U suppose to have 20x^-6. Its as simple as that.
Now wat if u had sumting like 2/3x^4, how wud u differentiate that. Confused???? Don’t be. Again bring it to a polynomial. U wud get 2/3x^-4. this is two thirds x to the minus 4 if u didn’t kno. From here jus differentiate as normal. That’s 8/3 x ^-5. Got that???? Its so simple. If u don’t understand my explanation…as moose wud say YUH BAKE… YUH BAKE!!!!!
OH AH 4GET
QUIZ!!!!!
Differentiate!!!!
1) Y = 15x^4 - 5/2x3 – 3x
Differentiation of logs is very simple!!! Don’t hut yuh head. Nothings hard!!!!
Wat if u had to differentiate
y = log ( 5x^3) wat wud u do??? U just have to kno the formula
1/u X du/dx log e. In this case
u = 5x^3… du/dx = 15x^2. Just substitute these into the formula. For dy/dx U wud get
1/ 5x^3 X 15x^2 log e,
which can be expressed as
15x^2 / 5x^3 log e, Now wat if u had to differentiate
y = log 5x^3 + 11x ??? Remember there are no brackets. Remember brackets have meaning.!!!!! Wat wud your “u” be in this case???? Remember 5x^3 + 11x are two terms and not one. It wud have only been 1 term if there were brackets
(5x^3 + 11x). Understand????? So your “u” wud be 5x^3. Now just do as as showed u above. du/dx = 15x^2. so for dy/dx u wud get
1/ 5x^3 X 15x^2 log e which can be expressed as
15x^2 / 5x^3 log e,. But remember u also had 11x to differentiate. Jus find the differential of 11x which is 11 and jus plus it to
15x^2 / 5x^3 log e, so u wud get
15x^2 / 5x^3 log e + 11. Please note that in the function
y = log 5x^3 + 11x…..11x is independent of log 5x^3. 11x has nothing to do wit log 5x^3. OK!!!!!
Let me mix up tings a bit!!! Wat if u had to differentiate y = log to base 3 5x^3 + 11x wat wud u do?? Don’t be confused. Just work with the formula. It doesn’t matter wat the base is…it has nothing to do with the question. So ur answer wud be
dy/dx = 15x^2/ 5x^3 log to base 3 e + 11
GET IT????????
Diffentiation of ln functions follows the same pattern as logs as u wud see but is a little simplier The formula for finding dy/dx is 1/u X du/dx. It is simplier isn’t it??? Im sure ur licking ur lips!!!! Try differentiating y = ln x ^9 + x. Use the same pattern as u used in differentiating logs. Your “u” wud be x^9, your du/dx wud be 9x^8. True??? Just substitute into the formula now. U wud get 1/x^9 X 9x^8. Simple as that. Don’t 4get u have to differentiate x which is 1 so ur final answer wud be
1/x^9 X 9x^8 + 1 which can be expressed as 9x^8/x^9 + 1. UNDERSTAND??????
to miss i belive that that not all student are able to comments on sttarties to teach on certain topics such as differentiation of polynomials because they are a little confuse about it.could you help assist such students.
if i am teaching a subject such as differtiation of polynomial i would first start of with a simple example such as find the derivative of y = 8x^2
applying dy/dx where y is 8x^2
it will be d(8x^2)/dx
you then mulitply 2 x 8 = 16
and you minus 1 from 2=1 it is then totally = to 16x^1
cokebaby,....., that explanation real long dred. everthing yuh put was correct, xcept that in the third paragraph, the rel answer is -20x^-6. everything else , i suppose correct.
cokebaby ,cokebaby ,cokebaby do not miss interpret the function of the blog please
refrain from using the harsh words
to CAP VEG i will admit that i have made some of the silliest mistakes during quizzes the thing is for me i take for granted that i know a topic fullly.
i guess i need to take POP quizzes a little more seriously since it shows of my knowledge
To Cokebaby (ALONE):
In addition to moose's comment on March 5, 2008 3:25 PM
Please do not undermine the integrity of this blog. By calling me names and reffering to this blog as a 'game' proves that you have misjudged the purpose of this blog in its entirety. This blog is far from a game or any competition of the sort. I am not competing with you. We are suppose to be helping each other to grap mathematical concepts in a CONSTRUCTIVE environment. Someone of your intelligence should know that. I must now waste my time and a comment space to say all of this on the account of your unsolicited speech.
PULL YOURSELF TOGETHER MAN!!!
To Moose:
Not only you sir are affected by this. We as student must realise that an examination is mentally taxing. We as students should not disreguard the mental aspects associated with an exam. You yourself reguarded the errors as silly. However during the exam you probably would have seen it correct. This is one side effect of the mental taxing element an exam can produce.Good sir would you not agree?
To captain vegetable , the real purpose of this blog is for you to ask questions which are maths based , help other people on the blog understand what you know and share your knowledge for people who are weak in maths , like my self
will my strategy is to make it as easy as posible by relating it to other topics, so u can reflect and remember.
on the elemination fo errors in differentiation: u have to look at the signs carefully (+,-),because it is normaly forgot. all ways remember the basic.
im very very very sorry captain vegatable!! i was just tryn to be funny.i always do. I dont have anyting against u. I want 2 learn and im indeed learning quite alot from u. ur really helping me. tanks. sorry about that..Anyway back to the important stuff
sorry again captain vegetable!! with respect to ur question
y= log[5] (x^4-9x^-2+x+3.25)
dis is easy.
using the formula
dy/dx = 1/u x du/dx log e
u = (x^4-9x^-2+x+3.25)
du/dx = 4x^3 + 18x^-3 + 1
dy/dx = 1/(x^4-9x^-2+x+3.25)x 4x^3 + 18x^-3 log [5} e
ur final answer wud be
dy/dx = 4x^3 + 18x^-3/(x^4-9x^-2+x+3.25)log [5} e
Am i correct.
WAT IF I HAD TO DIFFERENTIATE
y= log[5] x^4-9x^-2+x+3.25
wat wud i get?????
i believe the differentiation of a polynomial to be easy-ish...
but most of us encounter problems wen the number is a fraction.. ex. 7/2x(3)... anyone can show how to differentiate that term?? i am the teacher so i can put questions..
also to as a teacher.. if i teach n explain somethin to the students in class... i would constantly probe them wit questions.. perhaps like arirosa said give them surprise the very next class.... and start simple from the laws of differentiation...
I haven't read everyone's comments yet, but thus far no one has explained exactly what a polynomial is i would imagine if you are explaing how to solve polynomials, you would breifly run through what a polynomial is / means or how to identify a polynomial in the first place. That is the very firstt step in solving anything,right. Identifying it.
To Moose - exactly where did the -4come from before the 4/5 in the second to last line in your commen?
every 1 is commenting on how they would handle som1 who cant seem 2 cope with d differentiation of polinomials and almost all d comments say that such person needs to understand the basis of polynomials. they must also understand the basic of exponents and the use of them there4 persons who dont understand they will hav a better comprehension of what is tryin 2 b said
To CRIMSON CROCK:
That is quite true we must identify the polynomial in the first place befor we differentiate
it. So to that extent a polynomial can be described as an expression (not an equation) that is formulated from a combination of variables (x,y,z) and constants (1,2,3,4). What also must be known especially for differentiation is that the combinations formed must be derived only from addition, subtraction and multiplication NOT division. lets take an example:
3x^2 + 2a - 7. This is a polynomial because it is a combination of variables and constants. Also They are formed using only addition, sutraction and multiplication. Now lets take this example: x^3 + 2 /x + 8x^2. This expression in its entirety is NOT a polynomial because it has a division sign in that exprssion.
To: CRIMSON CROCK
In addition to my last comment:
Remember when we had the famous expression such as 3/x^2 and was told to differentiate it. We know in the thinking process that we must bring the denominator to the top and then differentiate. What we are actually doing is converting that expression into a polynomial format. That is why it could not be differentiated in its expression format. REMEMBER from what we learned that the differentiation process can only apply to polynomials. So when expressions are given that are not polynomials we must convert it into a polynomial format. Would you not agree?
What you have to do is when you dis cover errors you must highlight them to the person or persons that made them and then explain the solution to them.
TO: Cool-face
Yes sir let me have a go at your question:
Firstly the expression:7/2x(3)
I am assuming that the 3 is an exponent.
This expression must first be converted into a polynomial so:
7/2x(3) should be writen as:
7/2 x 1/x^3. Now for the actual conversion into a polynomial:
We bring the denominator as the numerator and get the polynomial:
7/2 x x^-3 (please excuse the syntax). NOTE (the question at some point should have said that it is equal to y or some letter of the alphabet so we would know what we are differentiating with respect to x so I will assume it is y)
So now that we have the polynomial 7/2 x x^-3 which can also be written as 7/2x^-3 we diffrenciate as normal so we get something like this:
-3(7/2x)^-3-1 This is simplified to: -21/2 x x^-4. I wrote it in this way so it would not appear that the x^-4 is part of the denominator. Good lad would you not agree with the above.
"so in continuation if u are asked to differentiate let us say
y = 4/5x^4
jus simply rearrange to
y = 4/5 (x^-4)
dy/dx =
-4 x 4/5 (x^-4-1)
which is
-16/5(x^-5)
voila "
moose how u get dat ? i loss afta u rearrange
if i was teaching someone differentation of a logs question, first i'll make them find u, then find the differential of u, then put it in the formula dy/dx=1/u*du/dx loge.
y= log[5] (x^4-9x^-2+x+3.25)
dy/dx = 1/u x du/dx log e
u = (x^4-9x^-2+x+3.25)
du/dx = 4x^3 + 18x^-3 + 1
dy/dx = 1/(x^4-9x^-2+x+3.25)x 4x^3 + 18x^-3 log {5} e
dy/dx = 4x^3 + 18x^-3/(x^4-9x^-2+x+3.25)log [5} e
coke baby why place such long comments... i nearly fell asleep trying to read all that. Any way read every one comments including yours and i think it makes a lot of sense. FOR ME when teaching these three topics, u should go in the order from the most basic topics to the more complicated ones like u would teach logs before you teach ln and more out common errors in logs ,and then reapeat it in ln since it is related and see if the students can figure it. the same can be done for polynomials since i would teach it before logs
lilo how would you teach someone like me? i does learn the basics and then when learning something further into the topic i does forget the basics
to differentiate s = t ^n
step 1:bring the existing power down and use it to multiply.
step 2: reduce the old power by one and use it as the new power.
therefore ans: s = t^3
ds/dt = 3 t^3-1
= 3 t ^2
firstly you need to understand that differtiation enables us to determin how one quantity chamges with regard to another
well in order to teach someone, in think all will agree that you must firstly understand the person you are going to teach. i will teach by encouraging the person to ask questions. and then i will build on the knowledge the individual possess by asking him simple questions leading up to what i'm tryin to teach.
my strategy?
i would simply get to know my students capability when explaining the basics in logs and its formulas. then i'll gradually increase the level of question i give them when i reach polynomials and ln. the key for me is not to continue unless all of them are on the same page.
some common problems encountered are
1.dealing with negative numbers as the power
2.differentiating a unit power i.e when the power is one.
3.dealing with fractions.
1.follow the procedure mentioned
t = 2x^-3
dt/dx = -6x^-4 ( minus in a negative # from a negative number is the same as plus in a positve # if u remember the sign (-+)rules
2.s = t
ds/dt = 1t^0
= 1
3.f = 3/5x^2
= 3x-2/5
df/dt = -6x-3/5 it is kinda hard to c but u must understan that the 3/5 remains as a fraction and the x^2 wen brougth as the numerator becomes x^-2
To APOCALYPSE:
Apocalypse where have you gone? I hardly seeing you on this blog. I ask you a question for a while now and you still did not answer me. Please good sir lets talk before the curtains are drawn for this blog.
oh , yeah. well everyone has there own ability to learn a topic and there own method. errors are common among everyone.well i think that one way to prevent common errors is to probably attempt the questions you have trouble with. i know every teacher would say that but if you really attempt the same questions with different variables over a number of times you would realize that it sticks in your head. that was the purpose of giving assignment at large quantities, to understand what you are doing. so for the accomplishment of the certain topic, do questioins and if you get stick in one, ask the teacher for help in simple terms and then do the question again. believe me, it works.
so for the differentials, just follow the rules and attempt many questions and the method will stick in your head. same applies for the logs and ln functions.
that is what i think would work for everyone.
honestly i didnt understand how to differentiate properly but after reading cokebabys explaination things seem to be mush more clear so i wod advise anyone who are having diffculty to read the comments. Good lookin out cokebaby
In differentiation as captain vegetable rightfully said, when x by itself is differentiated it is always understood as 1. This is a mistake I always seem to make all the time.Be carefull
As captain vegeatble also said in his example
5/2x^3
y=5(2x^-3)
because you would need to re write this in a form which is easier to evaluate.
by definition A teacher is someone acknowledged as a guide or helper in processes of learning. A teacher who teaches on an individual basis may be described as a tutor.
thus a teacher such be able to allow students to build on their previous background knowledge about a partticular topic or one closely related.
Then introduce the simple questions, give assignments and quizzes on the very topic next class.Now do the assessment and stress on the mistakes observed.
The objective is typically a course of study, lesson plan, or a practical skill, including learning and thinking skills.
Now use an incentive to continue to motivate students in doing well & avoiding errors; while emphasing the important of doing well in the real world.
if i were to teach on the listed topics above i would first teach on what is differentiation and then come around to these subtopics gradually
in differenciating a polynomial the first thing u have to do is recognise that it is a polynomial. it must be in the form y=ax^n.
dy/dx can be found by multiplying the power by the coefficient, then minus 1 from the power. For example if y = 5x^9
dy/dx = 45x^8
hope u understand students.....
to captain vegetable:
to discuss polynomial differentiation, i would first introduce the delta process to the students.... and i would ensure they fully understand it then show the link with differentiation
to sparkle
why would you teach the student the delta process? why dont you just show them how to use the formula? dont you think the delta process will confuse the student more?
to sparkle
do you really find it necessary to teach the students the delta process? dont you think that's irrevelant to the topic?
well i was never made to be a teacher im more of a problem solver so no comments but cokebaby is the boss. that comment was reeealll dread. big up cokebaby
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