higher-order partial derivatives
(60 minutes to learn)
When we take partial derivatives of partial derivatives, we get what are known as higher-order partial derivatives. This can describe local properties of a function which aren't captured by the first-order approximation.
This concept has the prerequisites:
Core resources (read/watch one of the following)
→ Multivariable Mathematics
A textbook on linear algebra and multivariable calculus with proofs.
Location: Section 3.6, "Higher-order partial derivatives," pages 120-124
Supplemental resources (the following are optional, but you may find them useful)
→ Multivariable Calculus
An introductory multivariable calculus textbook.
Location: Section 13.4, "Partial derivatives," subsection "Higher-order partial derivatives," pages 874-875
- The single-dimensional Taylor approximations can be generalized to the multivariate case .
- create concept: shift + click on graph
- change concept title: shift + click on existing concept
- link together concepts: shift + click drag from one concept to another
- remove concept from graph: click on concept then press delete/backspace
- add associated content to concept: click the small circle that appears on the node when hovering over it
- other actions: use the icons in the upper right corner to optimize the graph placement, preview the graph, or download a json representation