trig derivative

**delgeezee** · October 13th 2011, 05:04 PM

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

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

**skeeter** · October 13th 2011, 05:09 PM

Originally Posted by delgeezee

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

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

$\frac{d}{dx} (\cos{x})^3 = 3(\cos{x})^2 \cdot (-\sin{x})$

**pickslides** · October 13th 2011, 05:11 PM

You need to use the chain rule here

Find $(\cos^3x)'$

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

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

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

Can you finish it?

**esander4** · October 13th 2011, 05:13 PM

Chain rule. 3(cosx)^2(-sinx)

**delgeezee** · October 13th 2011, 05:22 PM

Thanks, I understand now.

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