# How do you differentiate f(x) = e^(-5x^2)?

Jan 20, 2016

$- 10 x {e}^{- 5 {x}^{2}}$

#### Explanation:

Finding derivatives in the form ${e}^{u}$ is quite simple.

According to the chain rule,

$\frac{d}{\mathrm{dx}} \left[{e}^{u}\right] = {e}^{u} \cdot u '$

Thus,

$f ' \left(x\right) = \frac{d}{\mathrm{dx}} \left[{e}^{- 5 {x}^{2}}\right] = {e}^{- 5 {x}^{2}} \cdot \frac{d}{\mathrm{dx}} \left[- 5 {x}^{2}\right] = - 10 x {e}^{- 5 {x}^{2}}$