Find the derivative of the function $sec(tan \sqrt{x})$ with respect to $x$

The correct answer is $\dfrac{1}{2 \sqrt{x}}$ $sec(tan \sqrt{x})$ $tan(tan \sqrt{x})$ $sec^2(\sqrt{x})$

Let $y = sec(tan \sqrt{x})$

Using chain rule,

$\dfrac{dy}{dx}$ = $sec(tan \sqrt{x})$ $tan(tan \sqrt{x})$ $sec^2(\sqrt{x})$ $\dfrac{1}{2 \sqrt{x}}$


= $\dfrac{1}{2 \sqrt{x}}$ $sec(tan \sqrt{x})$ $tan(tan \sqrt{x})$ $sec^2(\sqrt{x})$