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Terms and Concepts 23. g(r) = 4' 1. T/F: The Chain Rule describes how to evaluate the deriva- 24. g(t) = 5cost tive of a composition of functions. 2. T/F: The Generalized Power Rule states that (g(x)") = 25. g(t) = 152 ng (x ) ) ". 26. m(w) = = 3 W 2 w a ( In(x) ) = 2. 3. T/F: 1 27. h(t) = 2 + 3 3t + 2 4. T/F: (3*) ~ 1.1 . 3*. 28. m(w) = 3" + 1 2 w dx 5. T/F: dy dx dt dt dy 29. f(x) = 3* + x 6. f ( x) = (Inx + x2)3 2 x 2 30. f(x) = x2 sin(5x) Problems 31. f(x) = (x2 + x) 5(3x4 + 2x) 3 In Exercises 7 -36, compute the derivative of the given func- tion. 32. g(t) = cos(t? + 3t) sin(5t - 7) 7. f ( x) = (4x3 - x) 10 33. f(x) = sin(3x + 4) cos(5 - 2x) 8. f(t) = (3t - 2) 5 34. g(t) = cos( )e512 9. g(0) = (sin 0 + cos 0)3 35. f ( x ) = sin (4x + 1) 10. h(t) = e312 +t-1 (5x - 9)3 11. f(x) = (Inx + x2)3 36. f(x) = (4 x + 1) 2 tan (5x) 12. f (x) = 2x3 + 3x In Exercises 37 -40, find the equations of tangent and normal 13. f ( x) = (x+ 4)4 lines to the graph of the function at the given point. Note: the functions here are the same as in Exercises 7 through 10. 14. f(x) = cos(3x) 15. g(x) = tan(5x) 37. f(x) = (4x3 - x) 10 at x = 0 16. h(0) = tan (02 + 40) 38. f(t) = (3t - 2)5 att = 1 17. g(t) = sin (+ + !) 39. g(0) = (sin 0 + cos 0)3 at 0 = T/2 18. h(t) = sin* (2t) 40. h(t) = e3 +t-1 att = -1 19. p(t) = cos'(+2 + 3t + 1) 41. Compute - ( In(kx)) two ways: 20. f(x) = In(cos x) (a) Using the Chain Rule, and 21. f(x) = In(x2) (b) by first using the logarithm rule In(ab) = Ina + Inb, 22. f( x) = 2 In(x) then taking the derivative