Understanding Multivariable Calculus: Problems, Solutions, and Tips
Limits, Continuity, and Partial Derivatives
S1 E3:
Apply fundamental definitions of calculus to multivariable functions, starting with their limits. See how these limits become complicated as you approach them, no longer just from the left or right, but from any direction and along any path. Use this to derive the definition of a versatile new tool: the partial derivative.