# How do you differentiate y=5e^x+3?

Apr 8, 2018

$\frac{d}{\mathrm{dx}} \left(5 {e}^{x} + 3\right) = 5 {e}^{x}$

#### Explanation:

This is a nice one to differentiate.

You can watch this Proof that shows why the derivative of ${e}^{x}$ is just equal to ${e}^{x}$; then, we can just differentiate the rest of the equation.

The derivative of any constant is equal to zero since the slope of any constant value is zero (a straight horizontal line equal to that value).

Then we treat the exponential plus its coefficient using the Power Rule.

$\frac{d}{\mathrm{dx}} \left(5 {e}^{x}\right) = \frac{d}{\mathrm{dx}} \left(5\right) \cdot {e}^{x} + 5 \cdot \frac{d}{\mathrm{dx}} \left({e}^{x}\right) = \left(0\right) \cdot \left({e}^{x}\right) + \left(5\right) \cdot \left({e}^{x}\right)$
$= 5 {e}^{x}$