Question

Differentiate the following functions with respect to x

$cos\left(\sqrt{x}\right)$

Answer 1

Ley y = $cos\left(\sqrt{x}\right)$

Differentiate both sides w.r.t. x

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

[Using chain rule $\frac{d}{dx}f\left(g\right(x\left)\right)=f^{\prime }\left(x\right)\frac{d}{dx}g\left(x\right)$]

= $-sin\sqrt{x}\frac{1}{2\sqrt{x}}=-\frac{sin\sqrt{x}}{2\sqrt{x}}$