Question

Differentiate given problems w.r.t.x.

$si{n}^{-}1\left(x\sqrt{x}\right),0\le x\le 1$.

Answer 1

Let y = $si{n}^{-}1\left(x\sqrt{x}\right)$

Differentiating w.r.t.x, we get

$\frac{dy}{dx}=\frac{d}{dx}\left(si{n}^{-}1x\sqrt{x}\right),0\le x\le 1$

$\frac{dy}{dx}=\frac{\frac{d}{dx}\left(x^3/2\right)}{\sqrt{1-(x\sqrt{2}{)}^2}}\Rightarrow \frac{dy}{dx}=\frac{\frac{3}{2}\left(x^1/2\right)}{\sqrt{1-x^2}}\to \Rightarrow \frac{dy}{dx}=\frac{3}{2}\frac{\sqrt{x}}{\sqrt{1-x^3}}$