# Differentiate the functions with respect to $x$: $sec \;( tan (\sqrt x ) )$
$\begin{array}{1 1} \frac{1}{2\sqrt x}.sec (tan\sqrt x). tan (sec\sqrt x) (sec^2\sqrt x) \\ \frac{-1}{2\sqrt x}.sec (tan\sqrt x). tan (sec\sqrt x) (sec^2\sqrt x) \\ \frac{1}{2\sqrt x}.sec (sec\sqrt x). tan (tan\sqrt x) (sec^2\sqrt x) \\ \frac{1}{2\sqrt x}.sec (sec\sqrt x). tan (sec\sqrt x) (sec^2\sqrt x) \end{array}$