Question

What is arcsin derivative?

Answer 1

Derivative of trigonometric inverse function:

Arcsin means the inverse of the sin function.

The derivative of arcsin is,

$\frac{d}{dx}\left(a\mathrm{rcsin}\left(\mathrm{x}\right)\right)=\frac{d}{dx}\left({\sin }^{-1}\left(x\right)\right)$ $[x\mathrm{is}a\mathrm{variable},-1\le x\le 1]$

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

Hence,derivative of $\mathit{a}\mathit{r}\mathit{c}\mathit{s}\mathit{i}\mathit{n}\mathbf{\left(}\mathit{x}\mathbf{\right)}$ is $\frac{\mathbf{1}}{\sqrt{\mathbf{1}\mathbf{-}{\mathbf{x}}^{\mathbf{2}}}}$.