Question

Differentiate

$\left(si{n}^{-1}x\right)logx$

Answer 1

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

Differentiate on both sides w.r.t x

$\frac{dy}{dx}=\frac{d}{dx}\left(si{n}^{-1}\right(x\left)\right)logx+si{n}^{-1}x\left(\frac{d}{dx}\right(logx\left)\right)$

$=\frac{logx}{\sqrt{1-x^2}}+\frac{si{n}^{-1}\left(x\right)}{x}$

$\therefore \frac{dy}{dx}=\frac{logx}{\sqrt{1-x^2}}+\frac{si{n}^{-1}\left(x\right)}{x}$