Question

Differentiate the following w.r.t.x:
${\cos }^{-1}\left(4\sqrt{x}\right)$

Answer 1

$y={\cos }^{-1}\left(4\sqrt{x}\right)$

Differentiating w.r.t. x,

$\frac{dy}{dx}=-\frac{1}{\sqrt{1-16x}}.\frac{d}{dx}\left(4\sqrt{x}\right)$

$\frac{dy}{dx}=-\frac{1}{\sqrt{1-16x}}.4\times \frac{1}{2}{x}^{-1/2}$

$\frac{dy}{dx}=-\frac{2}{\left(\sqrt{1-16x}\right)\left(\sqrt{x}\right)}$