Khan Academy

Vector form of the multivariable chain rule (K-A)

Directional derivatives (going deeper) (K-A)

Directional derivatives (introduction) (K-A)

Introduction to partial derivatives (K-A)

Second partial derivatives (K-A)

The gradient (K-A)

Formal definition of partial derivatives (K-A)

Graphical understanding of partial derivatives (K-A)

Partial derivatives, introduction (K-A)

Symmetry of second partial derivatives (K-A)

Computing the partial derivative of a vector-valued function (K-A)

Partial derivative of a parametric surface, part 1 (K-A)

Partial derivative of a parametric surface, part 2 (K-A)

Partial derivatives of vector fields (K-A)

Partial derivatives of vector fields, component by component (K-A)

Interpretation of Lagrange multipliers (K-A)

Lagrange multipliers, examples (K-A)

Lagrange multipliers, introduction (K-A)

Constrained optimization introduction (K-A)

Finishing the intro lagrange multiplier example (K-A)

Lagrange multiplier example, part 1 (K-A)

Lagrange multiplier example, part 2 (K-A)

Lagrange multipliers, using tangency to solve constrained optimization (K-A)

Meaning of the Lagrange multiplier (K-A)

Proof for the meaning of Lagrange multipliers (K-A)