This blog created by Fariel Mohan is to assist MATH110D students in understanding foundational mathematical concepts.
Monday, February 4, 2008
Derivative
What really is first derivative? Is first derivative any thing to do with differentation? Explain. What really is the use of firat derivative in maths? How can I understand first derivative in relation to the world?
Yeaa! im first..I tink derivative means finding dy/dx of a function , in other words differentiating a function.. For example the derivative of the function x raised to the power 2 is equal to 2x. Wat u all tink?
I think that the first derivitive includes finding dy/dx of a particular function. dy/dx is probably finding the gradient function of a curve. it is used in maths to find the gradient of a curve at a point. in relation to the real world dy/dx can help predict the outcome of a situation.
I think I agree with cokebaby when he says a derivative means finding dy/dx of a function.I learnt last week that a function x raised to the power for instance 3 is equal to3x.
i can only explain what is the first derivative with an example Dy/Dx 2x = 2 this is the first derivative. the second derivative D2y/Dx2 2 = 0 let me know if anyone confused
i think the derivative of a function has 2 do with the measure of change of the function when the intial values are changed. derivative can also be the rate of change of one value with respect to another value. for example, the rate of change of change of x with respect to y is given as dy/dx. derivatives can be used in the real world whereby the gradient of slopes can be calculated.
I agree that a derivative means finding dy/dx and a change in a particular function. But why do we have to find dy/dx of a function?? Is there some other way to solve the function??
In math, first derivative is used in finding the gradiant at a point on a curve. this is done by finding dy/dx of a function and then substituting an x value into dy/dx. Derivative can also be used in determining the stationary point on a curve. This is done by putting dy/dx = 0 and solving.
i think the first derivitive is simply the term which you differentiat first.For example if you had an expression like 2x + 3 , the first derivitive would be 2x. If anyone reads this comment, please correct me if i am wrong.
first derivative in relation to the world...this i tink involves rates of change, where dy/dx gives the rate at which y increases compared to x. This can be applied to almost any application. for example, the rate at which a sperical balloon is being blown up so that its volume increases at a constant rate of 2cm3 per second. The volume of a sperical bolloon in 4/3 pie r3. therefore dv/dr = 4pie r2
The derivative is a measurement of how a function changes when the values of its inputs change. or, a derivative can be thought of as how much a quantity is changing at some given point.example, the derivative of the position or distance of a truck at some point in time is the instantaneous velocity, or instantaneous speed, at which that car is traveling It describes the best linear approximation of the function near that input value. The process of finding a derivative is called differentiation. which is the reverse process to integration.
well, i know everyone knows what is the gradient of a curve, like, for example, of it is read off of a curve. the function obtained from the curve is the gradient function. this is the derivatibe and can be calculated by- y=2x(squared), the first derivative is dy/dx= 4x. the power multiplies by the coeffecient of x and then 1 is subtracted from the power, thus, 4x.
I am clueless about this particular topic! My only real introduction to first derivative was in Thursday's class 3 weeks ago. I understand how to work out problems of this nature but concept details, I have nothing much. Variable 47, kervin and tazmania are the persons who have my attention on their concepts so far.
a derivative can be thought of as how much a quantity change when the value of its input changes. For example, the derivative of the position or distance of a car at some point in time is the instantaneous velocity, or speed , at which that car is traveling
derivative is find the differential of a term.. dy/dx is the first derivative of a term or expresion... eg. 4x squared is 8x... wen findin the derivative u mulitiply the power by the coefficient and decrease the power by one.
well as i learn in class this is to my understanding dy/dx is the derivative and as i learn can be call instaneous rate of change and also the gradient imagine all this big words just to say its the gradient.
hey i have a qick question any one knows who came up with derivatives or even logs. interesting to know how smart these ppl was back then in the ages think we good reach there some day????????
first derivative is used in maths to dertemine the gradient or gradient expression of an equation of a curve or 'inlinear' function, at a specific instantaneous moment or point on the curve
Why are u commenting on the topic (second derivative).We are still on the first derivative and although I understand the second derivative I think that u may confuse others.
I really can't explain clearly what really is the delta process but all I can say is that it is differentiation by first principle and it is a really long method.
the first derivitive is the variation of one variable with respect to another.if the two variables were plotted on a graph the gradient of the graph would be the first derivitive
thanks poison for clearing that up and i agree with tigger because the first derivative is the differential of a certain function and when differentiating you differnetiate one thing with respect to another.
Yes first derivative deals with differentation this is because the first derivative is said to be the gradient an when you differentate you also find the gradient
yes i think first derivative has everything to do with differentiation since first derivative is the value you get when you differentiate a function for the first time meaning that you are finding dy/dx of a function. dy/dx is the rate of change of one value with respect to another as mentioned by tazmania and rate of change is gradient therefore dy/dx is used in finding gradient. for example dy/dx of 5x+2 is equal to 5 and 5 is also the gradient of the function i think.
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46 comments:
Yeaa! im first..I tink derivative means finding dy/dx of a function , in other words differentiating a function.. For example the derivative of the function x raised to the power 2 is equal to 2x. Wat u all tink?
derivitive dy/dx I dont quite understand how is this used in the delta process?
I think that the first derivitive includes finding dy/dx of a particular function. dy/dx is probably finding the gradient function of a curve. it is used in maths to find the gradient of a curve at a point. in relation to the real world dy/dx can help predict the outcome of a situation.
i agree with variable 47 that the first derivative is dy/dx, dy/dx is also the gradient function of a curve.
The derivative of a function represents an change in the function with respect to one of its variables.
i think derivative is the how much a quantity will change at a given point.
I think I agree with cokebaby when he says a derivative means finding dy/dx of a function.I learnt last week that a function x raised to the power for instance 3 is equal to3x.
why do we need differentiation. i dont see how it is related to real life! can someone enlighten me?
i can only explain what is the first derivative with an example Dy/Dx 2x = 2 this is the first derivative. the second derivative D2y/Dx2 2 = 0 let me know if anyone confused
i think the derivative of a function has 2 do with the measure of change of the function when the intial values are changed. derivative can also be the rate of change of one value with respect to another value. for example, the rate of change of change of x with respect to y is given as dy/dx. derivatives can be used in the real world whereby the gradient of slopes can be calculated.
I agree that a derivative means finding dy/dx and a change in a particular function. But why do we have to find dy/dx of a function?? Is there some other way to solve the function??
In math, first derivative is used in finding the gradiant at a point on a curve. this is done by finding dy/dx of a function and then substituting an x value into dy/dx. Derivative can also be used in determining the stationary point on a curve. This is done by putting dy/dx = 0 and solving.
i think the first derivitive is simply the term which you differentiat first.For example if you had an expression like 2x + 3 , the first derivitive would be 2x. If anyone reads this comment, please correct me if i am wrong.
first derivative in relation to the world...this i tink involves rates of change, where dy/dx gives the rate at which y increases compared to x. This can be applied to almost any application. for example, the rate at which a sperical balloon is being blown up so that its volume increases at a constant rate of 2cm3 per second. The volume of a sperical bolloon in 4/3 pie r3. therefore dv/dr = 4pie r2
well a derivative is where u derive something from so that means finding dy/dx of a function which has to do with differentation.
The derivative is a measurement of how a function changes when the values of its inputs change. or, a derivative can be thought of as how much a quantity is changing at some given point.example, the derivative of the position or distance of a truck at some point in time is the instantaneous velocity, or instantaneous speed, at which that car is traveling
It describes the best linear approximation of the function near that input value. The process of finding a derivative is called differentiation. which is the reverse process to integration.
well, i know everyone knows what is the gradient of a curve, like, for example, of it is read off of a curve. the function obtained from the curve is the gradient function. this is the derivatibe and can be calculated by- y=2x(squared), the first derivative is dy/dx= 4x. the power multiplies by the coeffecient of x and then 1 is subtracted from the power, thus, 4x.
I am clueless about this particular topic! My only real introduction to first derivative was in Thursday's class 3 weeks ago. I understand how to work out problems of this nature but concept details, I have nothing much. Variable 47, kervin and tazmania are the persons who have my attention on their concepts so far.
a derivative can be thought of as how much a quantity change when the value of its input changes. For example, the derivative of the position or distance of a car at some point in time is the instantaneous velocity, or speed , at which that car is traveling
a derivative is the change at a given point. for example the change in x with respect to y hence dy/dx.
i think the first deivative is in maths , is to find the gradient of a quadartic equation.
derivative is find the differential of a term.. dy/dx is the first derivative of a term or expresion... eg. 4x squared is 8x... wen findin the derivative u mulitiply the power by the coefficient and decrease the power by one.
The first derivative is basically the first differential of any equation whereby finding the gradient in the case of a quadratic equation
In calculus, the derivative is a measurement of how a function changes when the values of its inputs change.
I got a little bit confused this morning about the dy/ dx expression
To cruiser:
deritive dy/dx is just the shorterned method of calculating the gradient.
It is the same as the delta process (the longer way).
wel from my knowledge, the first derivaive is finding dy/dx of a function in order to attain the gradient.
MISS, CAN YOU GIVES US THE CORRECT DEFINITION OF THE FIRST DERIVITIVE.
well as i learn in class this is to my understanding dy/dx is the derivative and as i learn can be call instaneous rate of change and also the gradient imagine all this big words just to say its the gradient.
To cokebaby:
I am a bit confused about the first comment u gave on the blog.
What really is dy/dx of a function?
Please respond as quickly as possible.
hey i have a qick question any one knows who came up with derivatives or even logs. interesting to know how smart these ppl was back then in the ages think we good reach there some day????????
i agree with tazmania she has extended wat i said which is correct.the first derivative can be used in engineering.
what exactly is the delta process top shotter
first derivative is used in maths to dertemine the gradient or gradient expression of an equation of a curve or 'inlinear' function, at a specific instantaneous moment or point on the curve
To moose:
Why are u commenting on the topic (second derivative).We are still on the first derivative and although I understand the second derivative I think that u may confuse others.
To tweety:
I really can't explain clearly what really is the delta process but all I can say is that it is differentiation by first principle and it is a really long method.
to those who dont know what is delta process, delta process is simply differentiation without using the formula. it can be used to prove the formula.
the first derivitive is the variation of one variable with respect to another.if the two variables were plotted on a graph the gradient of the graph would be the first derivitive
thanks poison for clearing that up and i agree with tigger because the first derivative is the differential of a certain function and when differentiating you differnetiate one thing with respect to another.
the derivative is a measurement of how a function changes when the values of its inputs change.
in other words a derivative can be thought of as how much a quantity is changing at some given point.
Yes first derivative deals with differentation this is because the first derivative is said to be the gradient an when you differentate you also find the gradient
The first derivative is said to be the first defferential of a function
all of them saying they think an thing, but i am sure that the derivative means the dy/dx, where it is the change in gradient
bearing in mund that the derivative must be with respect to the function.
derivative is gradient which is also known as differentiation(dy/dx). the derivative is used to find the gradient of functions.
yes i think first derivative has everything to do with differentiation since first derivative is the value you get when you differentiate a function for the first time meaning that you are finding dy/dx of a function. dy/dx is the rate of change of one value with respect to another as mentioned by tazmania and rate of change is gradient therefore dy/dx is used in finding gradient. for example dy/dx of 5x+2 is equal to 5 and 5 is also the gradient of the function i think.
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