Chain Rule

Reference Page: #1 Univariate Chain Rule - ‘speeding up’ interperation. ‘boosting’ at a point

All derivatives are evaluated at the same point, just in different input domains

Multivariate chain rule, dx,dy can be separated due to linearization. Increases accumulate across dx, and dy.

extending to multi-in, multi-out viewing things in terms of unit changes after linearization.

Key Idea: we can think of moving dx in x, and then moving dy in y, and seeing how much f changes. This will be the same as moving in the directional derivative, since for linear functions, the slope is the same everywhere.

Key Idea: to compute df/ds, linearize everything, move one unit in s, and see how much that affects f.

The linearity assumption is the assumes that changes in variables will affect the output independently.

wherever a function has a derivative, it is locally linear

Last Reviewed: 10/27/24 Reference Page: #1