Partial Derivatives, Vs Ordinary Derivatives, Differentiability - Calculus 3

This video explains partial derivatives, including the limit definition, notation and analogy to ordinary derivatives, evaluating them (power, chain, product and quotient rules, implicit differentiation, etc), as the slope of the tangents to the curve, higher-order partial derivatives (second, third, etc), continuity and differentiability of functions of multi-variable functions, mixed derivative theorem (Clairaut's), and worked example practice problems.

0:00 Partial derivatives, definition
8:17 Evaluating partial derivatives
12:14 Partial derivatives of functions with more than two variables
14:46 Higher-order partial derivatives
19:57 Continuity and differentiability of multi-variable functions
26:13 Mixed derivative theorem, symmetry
29:27 Worked examples