# How do you find the derivative of e^(2y)?

Nov 29, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{2 x}$ Assuming: $x = {e}^{2 y}$

#### Explanation:

This queston is somewhat ambigious as is does not state the variable which we are to find the derivitive with respect to.

I will assume: $x = {e}^{2 y}$ and that we are seeking $\frac{\mathrm{dy}}{\mathrm{dx}}$

$x = {e}^{2 y}$

$\ln x = 2 y$

$y = \frac{1}{2} \ln x$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{2} \cdot \frac{1}{x} = \frac{1}{2 x}$

NB: If the question was intended to be: $\frac{d}{\mathrm{dy}} \left[{e}^{2 y}\right]$ the result would have been: $2 {e}^{2 y}$