Derivatives of multivariable functions

Lessons
Partial derivatives
Gradient and directional derivatives
Partial derivative and gradient (articles)
Differentiating parametric curves
Multivariable chain rule
Curvature
Partial derivatives of vector-valued functions
Differentiating vector-valued functions (articles)
Divergence
Curl
Divergence and curl (articles)
Laplacian
Jacobian
About this unit
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.