# How do you differentiate y=2e^x?

Nov 4, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 {e}^{x}$

#### Explanation:

You should know that the exponential function ,${e}^{x}$ where $e$ is Euler's Number (2.7182 ...), is the only function that remains unchanged when differentiated.

i.e $\frac{d}{\mathrm{dx}} \left({e}^{x}\right) = {e}^{x}$

So if $y = 2 {e}^{x} \implies \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{d}{\mathrm{dx}} \left(2 {e}^{x}\right)$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = 2 \frac{d}{\mathrm{dx}} \left({e}^{x}\right)$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = 2 {e}^{x}$