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Warm-up 2.4 Find the derivative of the following: 1) 2) 3)

Warm-up 2.4 Find the derivative of the following: 1) 2) 3). Lesson 2.4 The Chain Rule. 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:.

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Warm-up 2.4 Find the derivative of the following: 1) 2) 3)

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  1. Warm-up 2.4 Find the derivative of the following: 1) 2) 3)

  2. Lesson 2.4The 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”

  4. 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:

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

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

  7. Example 1 Find the derivative

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