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41. If f(x) = x²/(1 + x), find f"(1).

41. If f(x) = x²/(1 + x), find f"(1).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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
Transcribed Image Text: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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