# If y=sin^5x then what is dy/dx?

Oct 4, 2016

Use the chain rule

#### Explanation:

If $y = {\sin}^{5} x$, then Let $u = \sin x$,

Then $\frac{\mathrm{du}}{\mathrm{dx}} = \cos x$ and $y = {u}^{5}$ so $\frac{\mathrm{dy}}{\mathrm{du}} = 5 {u}^{4}$

Chain rule gives $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\mathrm{du}} \frac{\mathrm{du}}{\mathrm{dx}}$. so:
$\frac{\mathrm{dy}}{\mathrm{dx}} = 5 {u}^{4} \cos x = 5 {\sin}^{4} x \cos x$