# What is the derivative of  tan^2 (e^x)?

$2 {e}^{x} \tan \left({e}^{x}\right) {\sec}^{2} \left({e}^{x}\right)$
Note that ${\tan}^{2} \left({e}^{x}\right) = {\left(\tan \left({e}^{x}\right)\right)}^{2}$. Then, simply use the chain rule thrice:
$\frac{d}{\mathrm{dx}} {\tan}^{2} \left({e}^{x}\right) = \frac{d}{\mathrm{dx}} {\left(\tan \left({e}^{x}\right)\right)}^{2} = 2 \tan \left({e}^{x}\right) \cdot {\sec}^{2} \left({e}^{x}\right) \cdot {e}^{x} = 2 {e}^{x} \tan \left({e}^{x}\right) {\sec}^{2} \left({e}^{x}\right)$