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The Chain & General Power Rule Section 2.4 By Liz Labuzienski, Soee Kwon and Sue Kim

The Chain & General Power Rule Section 2.4 By Liz Labuzienski, Soee Kwon and Sue Kim. Chain Rule. If y changes dy / du times as fast as u , and u changes du / dx times as fast as x , then y changes dy / du · du / dx times as fast as x .

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The Chain & General Power Rule Section 2.4 By Liz Labuzienski, Soee Kwon and Sue Kim

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  1. The Chain & General Power RuleSection 2.4By Liz Labuzienski, Soee Kwon and Sue Kim

  2. Chain Rule • If y changes dy/du times as fast as u, and u changes du/dx times as fast as x, then y changes dy/du · du/dx times as fast as x. • In other words, dy/dx = dy/du · du/dx • The Chain Rule:

  3. Examples

  4. Examples

  5. General Power Rule • If y = (u(x))n, where u(x) is a differentiablefunctionand nis a rational number,then or, equivalently,

  6. Examples • Note: If u = 3x – 2x2, then f(x) = u3. This means that the derivative can be rewritten as 3u2u’, which may help in the simplifying process.

  7. Examples

  8. Trigonometric Functions and the Chain Rule

  9. Example • Note: In this example, the function is a composition of three functions, so the Chain Rule will need to be applied twice.

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