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Derivatives of Exponential and Inverse Trig Functions

Derivatives of Exponential and Inverse Trig Functions. Objective: To derive and use formulas for exponential and Inverse Trig Functions. Derivatives of Exponential Functions. We will use our knowledge of logs to find the derivative of . We are looking for dy/dx.

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Derivatives of Exponential and Inverse Trig Functions

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  1. Derivatives of Exponential and Inverse Trig Functions Objective: To derive and use formulas for exponential and Inverse Trig Functions

  2. Derivatives of Exponential Functions • We will use our knowledge of logs to find the derivative of . We are looking for dy/dx.

  3. Derivatives of Exponential Functions • We will use our knowledge of logs to find the derivative of . We are looking for dy/dx. • We know that is the same as

  4. Derivatives of Exponential Functions • We will use our knowledge of logs to find the derivative of . We are looking for dy/dx. • We know that is the same as • We will take the derivative with respect to x and simplify.

  5. Derivatives of Exponential Functions • We will use our knowledge of logs to find the derivative of . We are looking for dy/dx. • We know that is the same as • We will take the derivative with respect to x and simplify. • Remember that so

  6. Derivatives of Exponential Functions • This formula, works with any base, so if the base is e, it becomes but remember , so

  7. Derivatives of Exponential Functions • With the chain rule these formulas become:

  8. Example 3 • Find the following derivatives:

  9. Example 3 • Find the following derivatives:

  10. Example 3 • Find the following derivatives:

  11. Example 3 • Find the following derivatives:

  12. Example 3 • Find the following derivatives:

  13. Example 3 • Find the following derivatives:

  14. Example 3 • Find the following derivatives:

  15. Example 3 • Find the following derivatives:

  16. Example 4 • Use logarithmic differentiation to find

  17. Example 4 • Use logarithmic differentiation to find • Let

  18. Example 4 • Use logarithmic differentiation to find • Let

  19. Example 4 • Use logarithmic differentiation to find • Let

  20. Example 4 • Use logarithmic differentiation to find

  21. Example 4 • Use logarithmic differentiation to find

  22. Derivatives of Inverse Trig Functions

  23. Example 5 • Find dy/dx if:

  24. Example 5 • Find dy/dx if:

  25. Example 5 • Find dy/dx if:

  26. Homework • Page 254 • 11-21 odd • 27, 33-41 odd

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