is it -3sin^3(3x) or did i miss something?

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- Oct 6th 2012, 12:06 PMdanielsderivative of cos^3(3x)?
is it -3sin^3(3x) or did i miss something?

- Oct 6th 2012, 12:11 PMTheEmptySetRe: derivative of cos^3(3x)?
Yes you need to use the chain rule. Twice.

let

$\displaystyle f(u)=u^3$

$\displaystyle u=cos(v)$

and

$\displaystyle v=3x$

Then by the chain rule you get

$\displaystyle \frac{df}{dx}=\frac{df}{du}\frac{du}{dv}\frac{dv}{ dx}$

$\displaystyle 3u^2(-\sin(v))(3)=-9\cos^2(3x)\sin(x)$ - Oct 6th 2012, 12:16 PMdanielsRe: derivative of cos^3(3x)?
so then im guessing for f(x) = 2sin(2x) + e^(3x^2) + cos^3(3x)

f '(x) isn't= 4cos(2x) + 3e^(x^2) + -3sin^3(3x) ???? - Oct 6th 2012, 12:19 PMTheEmptySetRe: derivative of cos^3(3x)?
- Oct 6th 2012, 12:29 PMdanielsRe: derivative of cos^3(3x)?
okay thnks