Multivariable chain ruleMultivariable chain rule intuitionVector form of the multivariable chain ruleMultivariable chain rule and directional derivativesMore formal treatment of multivariable chain rule
Curvature intuitionCurvature formula, part 1Curvature formula, part 2Curvature formula, part 3Curvature formula, part 4Curvature formula, part 5Curvature of a helix, part 1Curvature of a helix, part 2Curvature of a cycloid
Computing the partial derivative of a vector-valued functionPartial derivative of a parametric surface, part 1Partial derivative of a parametric surface, part 2Partial derivatives of vector fieldsPartial derivatives of vector fields, component by component
2d curl intuition2d curl formula2d curl example2d curl nuanceDescribing rotation in 3d with a vector3d curl intuition, part 13d curl intuition, part 23d curl formula, part 13d curl formula, part 23d curl computation example
What does it mean to take the derivative of a function whose input lives in multiple dimensions? What about when its output is a vector? Here we go over many different ways to extend the idea of a derivative to higher dimensions, including partial derivatives, directional derivatives, the gradient, vector derivatives, divergence, curl, etc.