kreiranihqlz

2023-03-03

How to find the derivative of $z=x\left({y}^{2}\right)-{e}^{xy}$?

ajelyll

Beginner2023-03-04Added 2 answers

We have:

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

Which has the derivatives; which is a function of two variables;

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

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

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

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

Which has the derivatives; which is a function of two variables;

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

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

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