Implicit Differentiation

Abstract

Differentiate both sides as usual, but when encountering another (e.g ), write . That is, differentiate that function w/ respect to , then chain on a

We "view" as a function of and differentiate both sides of the equation with respect to .

Example

Differentiate

Simply apply the differentiation rules and "attach" a to each term

Derivatives of Inverses

Suppose we know the derivative of an invertible function .$

Definition

The derivative of an inverse function is:

only for first derivatives