# What is the derivative of e^(2xy)?

Apr 6, 2017

$\frac{d}{\mathrm{dx}} \left({e}^{2 x y}\right)$ or $\frac{d}{\mathrm{dt}} \left({e}^{2 x y}\right)$

#### Explanation:

With respect to $x$
$\frac{d}{\mathrm{dx}} \left({e}^{2 x y}\right) = \left({e}^{2 x y}\right) \frac{d}{\mathrm{dx}} \left(2 x y\right)$

$= \left({e}^{2 x y}\right) \left(2 y + 2 x \frac{\mathrm{dy}}{\mathrm{dx}}\right)$

With respect to $t$
$\frac{d}{\mathrm{dt}} \left({e}^{2 x y}\right) = \left({e}^{2 x y}\right) \frac{d}{\mathrm{dt}} \left(2 x y\right)$

$= \left({e}^{2 x y}\right) \left(2 y \frac{\mathrm{dx}}{\mathrm{dt}} + 2 x \frac{\mathrm{dy}}{\mathrm{dx}}\right)$