# How do you differentiate f(x)=sec^2(e^(x) )  using the chain rule?

$\frac{d}{\mathrm{dx}} {\sec}^{2} \left({e}^{x}\right) = 2 {e}^{x} {\sec}^{2} \left({e}^{x}\right) \tan \left({e}^{x}\right)$
$\frac{d}{\mathrm{dx}} {\sec}^{2} \left({e}^{x}\right) = \frac{d}{\mathrm{dx}} {\left[\sec \left({e}^{x}\right)\right]}^{2}$
$= 2 \sec \left({e}^{x}\right) \cdot \sec \left({e}^{x}\right) \cdot \tan \left({e}^{x}\right) \cdot {e}^{x}$