MAT 1234 Calculus I Section 2.5 Part II Chain Rule

Part II WebAssign HW 2.5 Part II (Do it early) Extended Power Rule –a special case of the chain rule Higher Derivatives (2.2)

Extended Power Rule u

u

u

Example 4

Example 5

More Examples on Chain Rules

Example 6 ( Product Rule, Chain rule, & Power Rule )

Example 7 ( Quotient Rule, & Ext. Power Rule )

Higher Derivatives

Example 8

Given a function f(x) which is a function. Higher Derivatives

Given a function f’(x) which is a function. Higher Derivatives

Given a function f’’(x) which is a function. Higher Derivatives

In general, we denote the n-th derivative of f(x) as Higher Derivatives

Notations

Example 9 Find if

Example 10