Section 3.4 The Chain Rule

Consider the function –We can “decompose” this function into two functions we know how to take the derivative of –For example –What are –Now think of as

Theorem 3.5: The Chain Rule Let g and f be differentiable functions then The derivative of a composite function is the derivative of the outside function (leaving the inside function alone) times the derivative of the inside function

Consider ___________ OUTSIDE FUNCTION: INSIDE FUNCTION: So we have:

The General Power Rule The General Exponential Rule

Examples