Study guide and 4 practice problems on:

## Chain rule with functions of several variables

The partial derivative of a composite function of multiple variables is $$\partial_a f(x(a, b), y(a,b)) = \partial_x f \ \partial_a x + \partial_y f \ \partial_a y$$
The total derivative of a composite function of multiple variables is $$\frac{d}{dt} f(t, x(t), y(t)) = \partial_t f + \partial_x f \ \frac{dx}{dt} + \partial_y f \ \frac{dy}{dt}$$