# How do you find the derivative of z=x(y^2)-e^(xy)?

Feb 27, 2017

$\frac{\partial z}{\partial x} = {y}^{2} - y {e}^{x y}$

$\frac{\partial z}{\partial y} = 2 x y - x {e}^{x y}$

#### Explanation:

We have:

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

Which is a function of two variables, so the derivatives are;

$\frac{\partial z}{\partial x} = {y}^{2} - y {e}^{x y}$

$\frac{\partial z}{\partial y} = 2 x y - x {e}^{x y}$

Remember when partially differentiating: differentiate with respect to the variable in question, treating the other variables as constant.