#41 060CHAPTER 3 DIFFERENTIATION RULES39. (a) If f(x) = (x² – 1)/(x2 + 1), find f'(x) and(b) Check to see that your answers to part (a) aby comparing the graphs of f, f', and f".40. (a) If f(x) = (x² – 1)e*, find f'(x) and f"(x).(b) Check to see that your answers to part (a) aby comparing the graphs of f, f', and f".41. If f(x) = x²/(1 + x), find f"(1).%3D42. If g(x) = x/e*, find g"(x).%3D43. Suppose that f(5) = 1, f'(5) = 6, g(5) = –3,Find the following values.(() (q)(c) (g/f)"44. Suppose that f(2) = -3, g(2) = 4, f'(2) = -(1() ()g'(2) =7. Find h'(2).(a) h(x) = 5f(x) –- 4g(x)%3D(4))f = (x)y (q)(x)645. If f(x) = e*g(x), where g(0) = 2 and g'(0)(x)4 ()- = (x)4 (P)46. If h(2) = 4 and h'(2) = -3, find

Answered: 41. If f(x) = x²/(1 + x), find f"(1).

Math

Calculus

41. If f(x) = x²/(1 + x), find f"(1).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 35E

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Question

#41

060
CHAPTER 3 DIFFERENTIATION RULES
39. (a) If f(x) = (x² – 1)/(x2 + 1), find f'(x) and
(b) Check to see that your answers to part (a) a
by comparing the graphs of f, f', and f".
40. (a) If f(x) = (x² – 1)e*, find f'(x) and f"(x).
(b) Check to see that your answers to part (a) a
by comparing the graphs of f, f', and f".
41. If f(x) = x²/(1 + x), find f"(1).
%3D
42. If g(x) = x/e*, find g"(x).
%3D
43. Suppose that f(5) = 1, f'(5) = 6, g(5) = –3,
Find the following values.
(() (q)
(c) (g/f)"
44. Suppose that f(2) = -3, g(2) = 4, f'(2) = -
(1() ()
g'(2) =7. Find h'(2).
(a) h(x) = 5f(x) –- 4g(x)
%3D
(4)
)f = (x)y (q)
(x)6
45. If f(x) = e*g(x), where g(0) = 2 and g'(0)
(x)4 ()
- = (x)4 (P)
46. If h(2) = 4 and h'(2) = -3, find

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