# How do you find the derivative of f(x) = e^x + e^(-x / 2)?

Feb 3, 2016

$f ' \left(x\right) = {e}^{x} - \frac{1}{2 {e}^{x}}$

#### Explanation:

Rule : $\frac{d}{\mathrm{dx}} {e}^{u \left(x\right)} = {e}^{u} \cdot \frac{\mathrm{du}}{\mathrm{dx}}$.

Application thereof :

$\frac{d}{\mathrm{dx}} \left[{e}^{x} + {e}^{- \frac{x}{2}}\right] = {e}^{x} - \frac{1}{2} {e}^{- x}$