Question

Differentiate the function tan $\sqrt{x}$ with respect to $X.$

Answer 1

Let $y=\tan \sqrt{x}$

Differentiating on both sides w.r.t $x$

$\frac{dy}{dx}=\frac{d\left(\tan \sqrt{x}\right)}{dx}={\text{sec}}^2\sqrt{x}\times \frac{d\left(\sqrt{x}\right)}{dx}={\text{sec}}^2\sqrt{x}\times \frac{1}{2\sqrt{x}}=\frac{{\text{sec}}^2\sqrt{x}}{2\sqrt{x}}$