how to solve dy/dx: cos*2X

Question

anonymous · Answer

derivative of cos (chain 2x)

anonymous · Answer

sin2x*2

anonymous · Answer

Are you sure, Starica is getting ready to correct you

anonymous · Answer

awww i thought we r to find dy/dx :S

anonymous · Answer

you just derive the outside and inside ^_^

outside = cos
inside 2x

so dy/dx of cos = -sin

and dy/dx of 2x = 2

soooo, dy/dx cos(2x) = -2sin(2x)

anonymous · Answer

o_o... but wasn't she right?

anonymous · Answer

no i missed the negative sign

anonymous · Answer

isn't it finding the derivative of cos(2x)?

anonymous · Answer

lol, it's alright :)

anonymous · Answer

i guessed it so

anonymous · Answer

you were close =P

anonymous · Answer

thanks:p

anonymous · Answer

np ^_^, do you get it now sandip?

anonymous · Answer

no its finding the derivative of cos^2x

anonymous · Answer

OH!

so the question is:

$$\frac{dy}{dx} \cos^2(x)$$?

anonymous · Answer

ya

anonymous · Answer

alright so we have 2 steps, first outside then inside, our outside here is the power and the inside is cos(x)

so dy/dx = - 2cos(x) sin(x) ^_^

anonymous · Answer

but star ...dont u think it must b y= cos^2x n find dy/dx??

anonymous · Answer

yeah lol

anonymous · Answer

wasn't I right? o_o

anonymous · Answer

... Go by the definition of the chain rule.

$$Let\ (cos\ x)^2 = f(g(x))$$

What is our f(x), what is our g(x)?

anonymous · Answer

she/he doesn't get the chain rule >_< lol

anonymous · Answer

in a much simpler way do it this way:

cos(x) . cos(x)

u'v + uv' ^_^ and solve

anonymous · Answer

I hope this way helps though :)

anonymous · Answer

alright gtg, later ^_^

anonymous · Answer

he-she isn't going to be able to do any of the rest of their homework if they don't understand the chain rule. This is a good opportunity to learn the chain rule since you need it to solve this problem.

anonymous · Answer

What can I say. Star likes manual labor.

anonymous · Answer

lol, I'm just trying to get it clear for him/her ^_^?