Chain Rule



THE CHAIN RULE: If and are both differentiable and is the composite function defined by then is differentiable and is given by the product



In Leibniz notation, if and are both differentiable functions, then



EXAMPLE: Find if


DIFFERENTIATION RULES




EXAMPLE: Find if .


EXAMPLE: Find if .


EXAMPLE: Find if .


EXAMPLE: Find if .


EXAMPLE: Find if .


EXAMPLE: Find if .


EXAMPLE: Find if .


EXAMPLE: Find if .


EXAMPLE: Find if .


EXAMPLE: Find if .


EXAMPLE: Find if
(a)
(b)
(c)

EXAMPLE: Find if .


EXAMPLE: Find if .


EXAMPLE: Find if .


EXAMPLE: Find if .


EXAMPLE: Find if .


EXAMPLE: Find if .

EXAMPLE: Find if .

EXAMPLE: Let

(a) Find .


(b) Find .


(c) Find .



COMMON MISTAKES


1.    WRONG!!!


2.    WRONG!!!