# Derivative of Implicit Multivariable Function – Calculating Derivative to a one variable function – Exercise 6474

Exercise

Given that the equation

$$xe^y+ye^x-e^{xy}=0$$

Defines the implicit function

$$y(x)$$

Find its derivative.

$$y'(x)=\frac{-e^y-ye^x+ye^{xy}}{xe^y+e^x-xe^{xy}}$$