thesaurus.maths.org

If f(x, y) is a function of both x and y, then the partial derivative of f with respect to x, written [(∂f)/(∂x)], is:

∂f ∂x = lim h → 0  f(x + h, y) − f(x, y) h

This is equivalent to differentiating with respect to x and treating y as though it were a constant. It can also be written f_x.
For example, if f(x, y) = x² + xy + 2 y²,
then [(∂f)/(∂x)] = 2 x + y
We can define partial derivatives with respect to z, and of functions of three or more variables, in the same way.