# How do you find the derivative of e^(xy) = 4?

Nov 19, 2016

Write in logarithmic form.

$\ln \left({e}^{x y}\right) = \ln 4$

$x y \ln e = \ln 4$

$x y = \ln 4$

$y + x \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) = 0$

$x \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) = - y$

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{y}{x}$

Hopefully this helps!