Question

Differentiate $\sin h^{-1}\left(\frac{1}{x}\right)$ with respect to $x(x>0)$

Answer 1

We need to find $\frac{d}{dx}\left(sin{h}^{-1}\left(\frac{1}{x}\right)\right)$

$\frac{d}{dx}\left(sin{h}^{-1}\left(\frac{1}{x}\right)\right)=-\frac{1}{x^2}\cdot \frac{1}{\sqrt{\frac{1}{x^2}+1}}=-\frac{1}{x^2}\cdot \frac{x}{\sqrt{x^2+1}}=-\frac{1}{x\sqrt{1+x^2}}$