1. 3.5 Chain Rule

2. Try this: Find if , right? What about this:
Isn’t this the same function as the previous slide, simply written differently?
How do we get the same answer from this expression? By the power rule, it should like where does the extra “4” come from?

3. The Chain Rule There are 2 versions: 1.
This says: If you see a function within a function, take the derivative of the outside function times the derivative of the inside.

4. Example of V1
Find if
Derivative of the inside – g’(x)

5. The Chain Rule The second version 2.
This says: if y is a function of u, and u is a function of x, then the derivative of y in terms of x will be the derivative of y in terms of u times the derivative of u in terms of x.
At the end, sub in the x expression in for u.

6. Example of V2
Find if and

7. Deriv of f(x) “outside”
Example
Find if and
Method 1:
Method 2:
Deriv of f(x) “outside”
Deriv of g(x) “inside”

8. Just follow the directions!!