Study guide and 15 practice problems on:

## Partial derivatives

Let $f(x,y)$ be a function of multiple variables. The partial derivative of $f$ with respect to $x$ evaluated at $(x,y)$ is the single-variable derivative obtained by differentiating $f(x,y)$ with respect to $x$ and treating all other variables as constants.
Notation: $\frac{\partial f}{\partial x}(x,y) = \partial_x f(x,y) = f_x(x,y)$.