Homework Help is Here – Start Your Trial Now!
Math
Calculus
Suppose that functions f and g and their derivatives with respect to x have the values shown to the right at x=2 and x= 3. Find the derivatives with respect to x of the combinations below at the given values of x. f'(x) g'(x) f(x) g(x) 2 2 5 3 -4 3 1 -7 27 3 f(x) g(x)' а. 2f(х), х%3D2 b. f(x) + g(x), x= 3 c. f(x) • g(x), x=3 с. d. x=2 1 e. f(g(x)), x=2 f. Vf(x), x=2 h. Px) +g°cx). x=2 g. x=3 gʻ(x) a. The derivative of 2f(x) with respect to x at x=2 is. (Simplify your answer. Type an exact answer, using a as needed.) b. The derivative of f(x) + g(x) with respect to x at x = 3 is D. (Type an exact answer, using a as needed.) c. The derivative of f(x) • g(x) with respect to x at x = 3 is (Type an exact answer, using z as needed.) d. The derivative of f(x) with respect to x at x=2 is g(x) (Type an exact answer, using z as needed.) e. The derivative of f(g(x)) with respect to x at x= 2 is (Type an exact answer, usinga as needed.) f. The derivative of yf(x) with respect to x at x=2 is (Type an exact answer, using z as needed.) 1 with respect to x at x= 3 is 9*(x) g. The derivative of . (TvDe an exact answer. usina z as needed.)

Suppose that functions f and g and their derivatives with respect to x have the values shown to the right at x=2 and x= 3. Find the derivatives with respect to x of the combinations below at the given values of x. f'(x) g'(x) f(x) g(x) 2 2 5 3 -4 3 1 -7 27 3 f(x) g(x)' а. 2f(х), х%3D2 b. f(x) + g(x), x= 3 c. f(x) • g(x), x=3 с. d. x=2 1 e. f(g(x)), x=2 f. Vf(x), x=2 h. Px) +g°cx). x=2 g. x=3 gʻ(x) a. The derivative of 2f(x) with respect to x at x=2 is. (Simplify your answer. Type an exact answer, using a as needed.) b. The derivative of f(x) + g(x) with respect to x at x = 3 is D. (Type an exact answer, using a as needed.) c. The derivative of f(x) • g(x) with respect to x at x = 3 is (Type an exact answer, using z as needed.) d. The derivative of f(x) with respect to x at x=2 is g(x) (Type an exact answer, using z as needed.) e. The derivative of f(g(x)) with respect to x at x= 2 is (Type an exact answer, usinga as needed.) f. The derivative of yf(x) with respect to x at x=2 is (Type an exact answer, using z as needed.) 1 with respect to x at x= 3 is 9*(x) g. The derivative of . (TvDe an exact answer. usina z as needed.)

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...
See similar textbooks
icon
Related questions
Question
Suppose that functions f and g and their derivatives with respect to x have the values shown to the right at x = 2 and x= 3. Find the derivatives with respect to x of the combinations below at the given values of x. g(x) f'(x) g'(x) f(x) 5 - 4 3 1 - 7 3 а. 2f(x), х%3D 2 b. f(x) + g(x), х%3D3 с. f(x) g(x), х%3D3 f(x) d. X =2 g(x)' 1 g. h. P(x) + g°(x), x=2 е. f(g(x)), х%3D2 f. Vf(x), x=2 X= 3 a. The derivative of 2f(x) with respect to x at x = 2 is (Simplify your answer. Type an exact answer, using t as needed.) b. The derivative of f(x) + g(x) with respect to x at x = 3 is (Type an exact answer, using t as needed.) c. The derivative of f(x) • g(x) with respect to x at x = 3 is (Type an exact answer, using a as needed.) f(x) with respect to x at x = 2 is g(x) d. The derivative of (Type an exact answer, using n as needed.) e. The derivative of f(g(x)) with respect to x at x = 2 is (Type an exact answer, using a as needed.) f. The derivative of vf(x) with respect to x at x = 2 is (Type an exact answer, using Tn as needed.) 1 g. The derivative of with respect to x at x = 3 is 2 gʻ(x) (Tvpe an exact answer. usina t as needed.)
Transcribed Image Text:Suppose that functions f and g and their derivatives with respect to x have the values shown to the right at x = 2 and x= 3. Find the derivatives with respect to x of the combinations below at the given values of x. g(x) f'(x) g'(x) f(x) 5 - 4 3 1 - 7 3 а. 2f(x), х%3D 2 b. f(x) + g(x), х%3D3 с. f(x) g(x), х%3D3 f(x) d. X =2 g(x)' 1 g. h. P(x) + g°(x), x=2 е. f(g(x)), х%3D2 f. Vf(x), x=2 X= 3 a. The derivative of 2f(x) with respect to x at x = 2 is (Simplify your answer. Type an exact answer, using t as needed.) b. The derivative of f(x) + g(x) with respect to x at x = 3 is (Type an exact answer, using t as needed.) c. The derivative of f(x) • g(x) with respect to x at x = 3 is (Type an exact answer, using a as needed.) f(x) with respect to x at x = 2 is g(x) d. The derivative of (Type an exact answer, using n as needed.) e. The derivative of f(g(x)) with respect to x at x = 2 is (Type an exact answer, using a as needed.) f. The derivative of vf(x) with respect to x at x = 2 is (Type an exact answer, using Tn as needed.) 1 g. The derivative of with respect to x at x = 3 is 2 gʻ(x) (Tvpe an exact answer. usina t as needed.)
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS