Question

Differentiate the function with respect to $x$
$\cos \left(\sqrt{x}\right)$

Answer 1

$\frac{d}{dx}\left[\cos \right(\sqrt{x}\left)\right]=-\sin \left(\sqrt{x}\right).\frac{d}{dx}\left(\sqrt{x}\right)$

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