Question

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

Answer 1

Let $f\left(x\right)=\sec \left(\tan \right(\sqrt{x}\left)\right)$
Thus using chain rule, we get
$f^{\prime }\left(x\right)=\frac{d\left[\sec \right(\tan \left(\sqrt{x}\right)\left)\right]}{d\left(\tan \right(\sqrt{x}\left)\right)}\cdot \frac{d\left(\tan \right(\sqrt{x}\left)\right)}{d\left(\sqrt{x}\right)}\cdot \frac{d\left(\sqrt{x}\right)}{dx}$
$=\sec \left(\tan \right(\sqrt{x}\left)\tan \right(\tan \left(\sqrt{x}\right)\cdot {\sec }^2\left(\sqrt{x}\right)\cdot \frac{1}{2\sqrt{x}}$