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2.4 The Chain Rule

2.4 The Chain Rule. "I recoil with dismay and horror at this lamentable plague of functions which do not have derivatives. -- Charles Hermite . Objectives:. To find derivatives using the chain rule. Two ways. Find the derivative of . A third way…. Chain rule

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2.4 The Chain Rule

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  1. 2.4 The Chain Rule "I recoil with dismay and horror at this lamentable plague of functions which do not have derivatives. -- Charles Hermite

  2. Objectives: • To find derivatives using the chain rule

  3. Two ways • Find the derivative of

  4. A third way… • Chain rule • y’ = deriv of outside (keep inside same) times deriv of inside • Example:

  5. A fourth way • Another form of the chain rule: • Example

  6. Example

  7. Another example

  8. What about trig functions? • Think of u substitution

  9. You try:

  10. More challenging examples…

  11. Another one • What rules will we use?

  12. Yet one more…

  13. Review: • Chain Rule:

  14. 2 more examples

  15. Last one

  16. Trig Chain Rule • Deriv of trig (keep angle same) deriv of angle • Be careful of double chain rule…

  17. Example

  18. Another example

  19. Three types…

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