# What is the derivative of c*(e^x) where c is a constant?

Jan 9, 2016

It is still $c \cdot \left({e}^{x}\right)$.

#### Explanation:

When calculating a derivative, multiplicative constants can always be brought outside of the expression:

$\frac{d}{\mathrm{dx}} \left[c \cdot \left({e}^{x}\right)\right] = c \cdot \frac{d}{\mathrm{dx}} \left[{e}^{x}\right]$

Since $\frac{d}{\mathrm{dx}} \left[{e}^{x}\right] = {e}^{x}$, the derivative of the entire function is exactly the same as how it started:

$\frac{d}{\mathrm{dx}} \left[c \cdot \left({e}^{x}\right)\right] = \textcolor{b l u e}{c \cdot \left({e}^{x}\right)}$