Question

What is the derivative of ${\sin }^{-1}\left(x\right)$?

Answer 1

Find derivative of ${\sin }^{-1}\left(x\right)$

Let $y={\sin }^{-1}x$

Differentiate it w.r.t $x$

$$\begin{gathered} \frac{dy}{dx}=\frac{d}{dx}{\sin }^{-1}\left(x\right) \\ =\frac{1}{\sqrt{1-x^2}},x\ne \pm 1 \end{gathered}$$

Hence, the derivative of ${\sin }^{-1}\left(x\right)$ is $\frac{1}{\sqrt{1-x^2}},x\ne \pm 1$.