4.1 the chain rule

Math Stuff

1. Warm-up Find the derivative of the following: 1) 2) 3)

2. Lesson 4.1 The Chain Rule

3. The Chain Rule Derivatives become complicated when we have composite functions Use a substitution, u = “the inside function” then Break up functions using the chain rule: “derivative of y in terms of u” “derivative of u in terms of x”

5. Steps: 1) Set u equal to an “inner” function 2) Rewrite original function in terms of u 3) Derive u in terms of x and y in terms of u 4) Plug derivatives into chain rule 5) Simplify Function form:

6. Example 1 Find the derivatives of the warm-ups using the chain rule

7. Since polynomials are prevalent we come up with a general power rule: derivative of outside function times derivative of inside function

8. Example 1 Find the derivative

9. Slopes of Parametrized Curves

10. Slide 3- 15 Finding dy/dx Parametrically