Monday, March 17, 2008

Differentiation of ln x, e^x, sin x, cos x

This section is for rate of change of ln x, e^x, sin x, cos x questions

17 comments:

cokebaby said...

miss!!!! wat this question really tryn to say. Are u asking me to differentiate those functions.
il differentiate it anyway.
i tink u all shud learn this, since its where differentiation of exponentials, trig and ln functions all begin.
if y = ln x
dy/dx = 1/x

if y = e^x
dy/dx = e^x

if y = sin x
dy/dx = cos x

if y = cos x
dy/dx = - sin x

U NEED TO KNOW THOSE!!!

cokebaby said...

ORRRR!!! I GET IT.. I WAS SUPPOSE TO ASK QUESTIONS!!! OK!!!!
I start very simple.
To anyone!!!!! differentiate
a) y = 2e^-2x

b) y = 2sin3x - 4cos3x^2

cokebaby said...

NOTE!!! To dirrerentiate an exponential function ie e^x..its just like normal differentiation.
Consider this example.
y = 4e^2x
find dy/dx
in this case we differentiate the power and multiply the differential by the coefficient and put back the remaining part of the function.
so dy/dy = 8e^2x

MOoSe said...

cokebaby;

DIFFERENTIATE

MOoSe said...

question
y = sin(x^2 + 3).

dy/dx = ??????

MOoSe said...

question 2
y = cos 3x^4.

dy/dx = ?????

it starting easy bloggers don't worry harder questions are coming

MOoSe said...

y = sin(e^3x)

dy/dx = ?????????

MOoSe said...

BLOGBAKES

y = e^(sin x).

dy/dx = ??????????

Tazmania said...

can anyone answer the following questions?
1) y=cos2x + x^2
find dy/dx

2) y=sin3x^4 . 3x
find dy/dx

apocalypse said...

cokebaby, :
1. y = 2e^2x.
so dy/dx = (2)2e^2x
= 4e^2x
2.y = 2sin 3x - 4cos 3x^2
for 2sin 3x:
in the form y= a sinx u, so u =3x and du/dx = 3
y = sin x, so dy/dx = cos x
i believe the constant remains the same.

MOoSe said...

taz

y = cos2x + x^2
let u = 2x
dy/du = 2
y = cosu + x^2
dy/du= -sin u

v = x^2
dv/dx = 2x
dy/dx= -sin 2x + 2x

master_cookie said...

WHY THE MASTER MUST ANSWER. I GETTING FED UP WITH THIS BLOG. but who cares
coming to Moose questions, i will be happy to answer the "harder ones".
question 1:

y = sin(e^3x)

let:

u = e^3x
du/dx = 3e^3x

therefore;
y = sin u
dy/du = cos u

this implies:

dy/dx = dy/du * du/dx
dy/dx = cos u * 3e^3x

dy/dx = (3e^3x)cos(e^3x)
and here ends question 1.

question 2:

y = e^(sin x)

let:
u = sin x
du/dx = cos x

therefore:

dy/dx = (cos x)(e^(sin x))

i will love for anyone to ask me any related questions PLEASEEEE.
i kind a bored nah so anytime u people want.

apocalypse said...

AHHHHHHH SOMEONE WHO IS WILLING TO ANSWER QUESTIONS!!!!!!!!!!!!
THAT IS WHAT I WANT TO HERE. A CHALLENGE

marz said...

y = sin(x^2 + 3)
dy/dx= cos x(2)2
dy/dx= 2 cosx(2)

hey can someone help me and correct me if im wrong cause i think i doing something wrong

But plz explain while you all show calculations it helps me much better

Dante' said...

well, marz.:
y = sin(x^2 + 3)
take u = (x^2 + 3)
du/dx = 2x
dy/du = cos u
dy/dx = dy/du x du/dx
dy/dx = cos u x 2x
dy/dx = 2xcos(x^2 + 3)
i think this right. is this right .......anyone????...

cruiser said...

ok cookie we all know you like to riight books
how do you know when to differentiate in terms of dy/dx??

Dante' said...

it all depends on the unknown variables in the equation, like in the equation of y that contains x variables: use dy/dx.