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Unit 3

Unit 3. More Derivatives. 3.1 Derivatives of Inverse Trig Functions. 3.1 Derivatives of Inverse Trig Functions. 3.1 Derivatives of Inverse Trig Functions. 3.1 Derivatives of Inverse Trig Functions. 3.1 Derivatives of Inverse Trig Functions. 3.2 Derivative of Exponential Functions.

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Unit 3

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  1. Unit 3 More Derivatives

  2. 3.1 Derivatives of Inverse Trig Functions

  3. 3.1 Derivatives of Inverse Trig Functions

  4. 3.1 Derivatives of Inverse Trig Functions

  5. 3.1 Derivatives of Inverse Trig Functions

  6. 3.1 Derivatives of Inverse Trig Functions

  7. 3.2 Derivative of Exponential Functions

  8. 3.2 Derivative of Exponential Functions

  9. 3.2 Derivative of Exponential Functions

  10. 3.3 Derivative of Natural Log Function

  11. 3.3 Derivative of Natural Log Function

  12. 3.3 Derivative of Natural Log Function

  13. 3.4 More Derivatives of Exponential and Logarithmic Functions

  14. 3.4 More Derivatives of Exponential and Logarithmic Functions

  15. 3.4 More Derivatives of Exponential and Logarithmic Functions

  16. 3.4 More Derivatives of Exponential and Logarithmic Functions Properties of Logarithms 1) 2) 3)

  17. 3.4 More Derivatives of Exponential and Logarithmic Functions Logarithmic Differentiation Take the natural log of both sides Simplify both sides using properties of logarithms Take the derivative of both sides Solve for dy/dx Substitute in for y.

  18. 3.4 More Derivatives of Exponential and Logarithmic Functions

  19. 3.4 More Derivatives of Exponential and Logarithmic Functions

  20. 3.5 Implicit Differentiation How do we find the derivative of a function that cannot be solved for y? 1. 2. 3. 4.

  21. 3.5 Implicit Differentiation

  22. 3.5 Implicit Differentiation

  23. 3.5 Implicit Differentiation

  24. 3.5 Implicit Differentiation

  25. 3.6 Inverses of Functions Reflect each function over the line y = x. f(x) g(x)

  26. 3.6 Inverses of Functions When does a function have an inverse? 1. 2. 3.

  27. 3.6 Inverses of Functions

  28. 3.6 Inverses of Functions f (x) f ˉ¹(x) (a, f (a)) → slope = f´ (a) →

  29. 3.6 Inverses of Functions

  30. 3.6 Inverses of Functions

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