Partial Derivatives

Partial Derivatives are derivatives in the direction of the axes.

f(x,y) = x^3 + y^2

 \dfrac {\partial f}{\partial x} = 3x^2

 \dfrac {\partial f}{\partial y} = 2y

We could technically do this for a function of one variable where there’s only one axis. We mention this because if we ever had the scenario we’re two ways of calculating derivative competed and conflicted with each other, the student would ask how do I know which one to use? It must be such that both will work, giving the same answer.