Partial Derivatives and the Jacobian
Extending Differentiation to Many Variables
How do we differentiate functions of multiple variables? This chapter builds the toolkit: partial derivatives, local linear approximation, differentiability, and the Jacobian matrix — the multivariable generalization of the derivative.
Sections
Limits and Continuity in Multiple Variables
10 min · 2 quiz questions
Partial Derivatives
10 min · 2 quiz questions · Interactive diagram
Partial Derivative Functions
8 min · 2 quiz questions
Continuously Differentiable Functions of Many Variables
8 min · 2 quiz questions
Symbolic Computation of Partial Derivatives
10 min · 2 quiz questions
Local Linear Approximation (Multivariate)
12 min · 2 quiz questions
Approximation Error and Differentiability
10 min · 2 quiz questions
Visualizing the Local Linear Approximation
8 min · 2 quiz questions · Interactive diagram
The Jacobian Matrix
12 min · 2 quiz questions · Interactive diagram
Jacobian: General Definition
8 min · 2 quiz questions
Linear Functions and the Jacobian
8 min · 2 quiz questions · Interactive diagram
Quadratic Functions and the Jacobian
10 min · 2 quiz questions