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

Jun 21, 2016

$f ' \left(x\right) = 5 {e}^{x}$

#### Explanation:

All that is here is a constant, $5$, multiplied with the function ${e}^{x}$. When differentiating a function that is multiplied a constant, just differentiate the other function and then multiply that by the constant.

Since the derivative of ${e}^{x}$ is also ${e}^{x}$, when you differentiate the function, the ${e}^{x}$ remains, and it is also multiplied by the $5$, giving the derivative of, again, $5 {e}^{x}$.

We can see this as:

$f ' \left(x\right) = \frac{d}{\mathrm{dx}} \left(5 {e}^{x}\right)$

Taking the constant out:

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

Since the derivative of ${e}^{x}$ is ${e}^{x}$:

$f ' \left(x\right) = 5 \cdot {e}^{x} = 5 {e}^{x}$