what it the derivative of $\displaystyle (cosX)^3 $ using rules

Is it as easy as $\displaystyle 3(-sinX)2 =-3sin^2X$ ?

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- Oct 13th 2011, 05:04 PMdelgeezeetrig derivative
what it the derivative of $\displaystyle (cosX)^3 $ using rules

Is it as easy as $\displaystyle 3(-sinX)2 =-3sin^2X$ ? - Oct 13th 2011, 05:09 PMskeeterRe: trig derivative
- Oct 13th 2011, 05:11 PMpickslidesRe: trig derivative
You need to use the chain rule here

Find $\displaystyle (\cos^3x)'$

Let's make $\displaystyle y=\cos^3x$ and $\displaystyle u=\cos x\implies y=u^3$

So $\displaystyle \frac{dy}{du} = 3u^2$ and $\displaystyle \frac{du}{dx} = -\sin x$

By the chain rule $\displaystyle \frac{dy}{dx}= \frac{dy}{du}\times \frac{du}{dx} $

Can you finish it? - Oct 13th 2011, 05:13 PMesander4Re: trig derivative
Chain rule. 3(cosx)^2(-sinx)

- Oct 13th 2011, 05:22 PMdelgeezeeRe: trig derivative
Thanks, I understand now.