A multi-variable function does not have a derivative but instead has multiple partial derivatives, one for each variable. The partial derivative is denoted by the $\frac{\partial }{\partial}$ symbol.

A function with two variables $f(x,y)$ has two partial derivatives:

• partial derivative with respect to $x$ = $\frac{\partial }{\partial x}f(x,y)$
• partial derivative with respect to $y$ = $\frac{\partial }{\partial y}f(x,y)$