# How do you find the derivative of y=e^(5x)?

Aug 4, 2014

$\frac{\mathrm{dy}}{\mathrm{dx}} = 5 {e}^{5 x}$

Process:

The derivative of ${e}^{x}$ is simply ${e}^{x}$. However, in this example, $x$ has a coefficient, so we will need to use the chain rule.

If $y = {e}^{5 x}$, then, by the chain rule, the derivative will be equal to the derivative of ${e}^{5 x}$ with respect to $5 x$, multiplied by the derivative of $5 x$ with respect to $x$.

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{d}{\mathrm{dx}} \left[5 x\right] \cdot {e}^{5 x}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 5 {e}^{5 x}$