# What is the derivative of y = arcsin(y^5)?

Feb 26, 2016

$\frac{5 {y}^{4}}{\sqrt{1 - {y}^{10}}}$

#### Explanation:

using the $\textcolor{b l u e}{\text{ chain rule }}$

and $\frac{d}{\mathrm{dx}} \left({\sin}^{- 1} x\right) = \frac{1}{\sqrt{1 - {x}^{2}}}$

hence $\frac{d}{\mathrm{dy}} \left({\sin}^{- 1} \left({y}^{5}\right)\right) = \frac{1}{\sqrt{1 - {\left({y}^{5}\right)}^{2}}} . \frac{d}{\mathrm{dy}} \left({y}^{5}\right)$

$= \frac{5 {y}^{4}}{\sqrt{1 - {y}^{10}}}$