# How do you differentiate e^tanx?

${e}^{\tan x} \cdot {\sec}^{2} x$
$\left(1\right) \frac{d}{\mathrm{dx}} \left({e}^{x}\right) = {e}^{x}$
$\left(2\right) \frac{d}{\mathrm{dx}} \left(\tan x\right) = {\sec}^{2} x$
$y = {e}^{\tan} x \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} = {e}^{\tan x} \cdot \frac{d}{\mathrm{dx}} \left(\tan x\right) , A p p l y \left(1\right)$
$\implies \frac{\mathrm{dy}}{\mathrm{dx}} = {e}^{\tan x} \cdot {\sec}^{2} x , A p p l y \left(2\right)$