Question

Find the derivative of cos²(√x).

Answer 1

Heard of chain rule?

Answer 2

no this new to me..

Answer 3

Well I suppose you to refer your study material to learn chain rule,you can't solve this question without that.

Answer 4

let's do that slowly :)
given y = cos²(√x)

Answer 5

@DLS my professor has not given us this assignment im just going ahead to learn it

Answer 6

okay,RadEn is proceeding so ill stay out of this :) good luck!

Answer 7

first, let u = √x = x^(1/2)
du/dx = 1/2 * x^(1/2 - 1) = 1/2 x^(-1/2) = 1/(2√x ), agree ??

Answer 8

okay got it :) thanks @RadEn

Answer 9

what, it's just the first step. not give us the final answer. lol

Answer 10

thanks @rizwan_uet

Answer 11

welcome

Answer 12

let's going to the 2nd step. (rizwan, u were incorrect :P)
Now we have :
y = cos²(u)

let v = cosu
dv/du = -sinu, agree ??

Answer 13

@320maria , also @rizwan_uet

Answer 14

yes i agree, sorry i didnt took the derivative of cos i m taking my answer back
reown the medal please @320maria

Answer 15

then finally,
now we have :
y = v^2
dy/dv = 2v

multiple of them (equations above) to get dy/dx
dy/dx = du/dx * dv/du * dy/dv
dy/dx = 1/(2√x ) * -sinu * 2v

dont forget, subtitute back that u = √x , and v = cos u = cos √x

so,
dy/dx = 1/(2√x ) * -sin(√x) * 2cos(√x)
dy/dx = - 1/√x * sin√x cos√x

Answer 16

\[\LARGE \cancel{2}\cos(\sqrt{x}) \times \sin \sqrt{x} \times \frac{-1}{\cancel 2 \sqrt{x}}\]
This is the final answer in one step with chain rule.

Answer 17

that's same like mine..
it just for the beginner only :)

Answer 18

yes its the same thing summed up
first the power,then function,then x