1.  3.8 Derivatives of Inverse Trigonometric Functions

2. Quick Review Slide 3- 2

3. Quick Review Slide 3- 3

4. Quick Review Solutions Slide 3- 4

5. Quick Review Solutions Slide 3- 5

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. Slide 3- 6

7. Derivatives of Inverse Functions Slide 3- 7

8. Derivative of the Arcsine Slide 3- 8

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

10. Example Derivative of the Arcsine Slide 3- 10

11. Example Derivative of the Arcsine Slide 3- 11

12. Derivative of the Arctangent Slide 3- 12

13. y = tan -1 (4x)

14. y = x tan -1 x

15. Derivative of the Arcsecant Slide 3- 15

16. Example Derivative of the Arcsecant Slide 3- 16

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 Slide 3- 19

21. Derivatives of Inverse Trig Functions Functionarcsin xarccos xarctan xarcsec x Derivative

22. Example Derivative of the Arccotangent Slide 3- 22

23. Calculator Conversion Identities Slide 3- 23

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

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

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

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

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

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

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

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

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