1. The Chain Rule (2.4)
September 30th, 2016

2. I. the chain rule
Thm. 2.10: The Chain Rule: If y = f(u) is a differentiable function of u and u = g(x) is a differentiable function of x, then y=f(g(x)) is a differentiable function of x and
-or-

3. Proof of Thm. 2.10: The Chain Rule
Prove

4. Alternate Proof of the Quotient Rule
Use the chain rule and the product rule to prove

5. II. The general power rule
Thm. 2.11: The General Power Rule: If , where u is a differentiable function of x and n is a rational number, then
-or-

6. Ex. 1: Differentiate each of the following functions.b) c) d) e)

7. Ex. 2: Use the graphs of f(x) and g(x) below to evaluate each of the following given that and .