Multivariate Calculus Tutorial 2 - Partial Derivatives

In this multivariate calculus tutorial we learn about the meaning of partial derivatives, calculate partial derivatives both via the limit definition and by using rules for differentiation. We differentiate functions partially using the product rule, the quotient rule, and the chain rule. Next we calculate the derivatives of implicitly defined functions, curves and surfaces. Finally, we calculate second partial derivatives and verify Clairaut's theorem with some examples.