# How do you find the derivative of sin^-1 * (5x)?

Aug 13, 2016

$\frac{5}{\sqrt{1 - 25 {x}^{2}}}$

#### Explanation:

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\frac{d}{\mathrm{dx}} \left({\sin}^{-} 1 x\right) = \frac{1}{\sqrt{1 - {x}^{2}}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

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

$\Rightarrow \frac{d}{\mathrm{dx}} \left({\sin}^{-} 1 \left(5 x\right)\right) = \frac{1}{\sqrt{1 - {\left(5 x\right)}^{2}}} . \frac{d}{\mathrm{dx}} \left(5 x\right)$

$= \frac{5}{\sqrt{1 - 25 {x}^{2}}}$