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3.8

3.8. Derivatives of Inverse Trigonometric Functions. Quick Review. Quick Review. Quick Review Solutions. Quick Review Solutions. What you’ll learn about. Derivatives of Inverse Functions Derivatives of the Arcsine Derivatives of the Arctangent Derivatives of the Arcsecant

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3.8

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  1. 3.8 Derivatives of Inverse Trigonometric Functions

  2. Quick Review

  3. Quick Review

  4. Quick Review Solutions

  5. Quick Review Solutions

  6. What you’ll learn about • Derivatives of Inverse Functions • Derivatives of the Arcsine • Derivatives of the Arctangent • Derivatives of the Arcsecant • Derivatives of the Other Three … and why The relationship between the graph of a function and its inverse allows us to see the relationship between their derivatives.

  7. Derivatives of Inverse Functions

  8. Derivative of the Arcsine

  9. Let f(x) = sin x and g(x) = sin-1x to verify the formula for the derivative of sin-1x.

  10. Example Derivative of the Arcsine

  11. Example Derivative of the Arcsine

  12. Derivative of the Arctangent

  13. y = tan-1 (4x)

  14. y = x tan-1x

  15. Derivative of the Arcsecant

  16. Example Derivative of the Arcsecant

  17. A particle moves along the x – axis so that its position at any time t ≥ 0 is given by x(t). Find the velocity at the indicated value of t.

  18. Assignment 3.8.1 page 170, # 3 – 11 odds

  19. Inverse Function – Inverse Cofunction Identities

  20. Derivatives of Inverse Trig Functions

  21. Example Derivative of the Arccotangent

  22. Calculator Conversion Identities

  23. Determine the derivative of y with respect to the variable.

  24. Determine the derivative of y with respect to the variable.

  25. Determine the derivative of y with respect to the variable.

  26. Determine the derivative of y with respect to the variable.

  27. Find an equation for the tangent to the graph of y at the indicated point.

  28. Find an equation for the tangent to the graph of y at the indicated point.

  29. Let f(x) = cos x + 3x Show that f(x) has a differentiable inverse.

  30. Let f(x) = cos x + 3x Determine f(0) and f’(0).

  31. Let f(x) = cos x + 3x Determine f-1(1) and f-1(1).

  32. y = cot-1 x Determine the right end behavior model.

  33. y = cot-1 x Determine the left end behavior model.

  34. y = cot-1 x Does the function have any horizontal tangents?

  35. Assignment 3.8.2 pages 170 – 171, # 1, 13 – 29 odds, 32 and 41 – 45 odds

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