1. 3.6 – The Chain Rule

2. The Chain Rule
If f and g are both differentiable and F = f • g is the composite function defined by F(x) = f(g(x)), then F is differentiable and F’ is given by the product
F’(x) = f’g(x)g’(x)
In Leibniz notation, if y = f(u) and u = g(x) are both differentiable functions then

3. Example 1
Find F’(x) if

4. Example 2
Differentiate
(a) y = sin(x2) (b) y = sin2x

5. Chain Rule + Power Rule If y = [g(x)]n, what is y’ ?
The Power Rule Combined with the Chain Rule
If n is any real number and u = g(x) is differentiable, then

6. Example 3
Differentiate

7. Example 4
Differentiate

8. Example 5
Differentiate