Let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 3, h'(1) = 4, g'(2) = 3, and f'(3) 7. Find r'(1) %3D %3D %3D r'(1) = %3D

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...
Question
Let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 3, h'(1) = 4, g'(2) = 3, and f'(3) = 7. Find r'(1)
%3D
%3D
%3D
%3D
%3D
r'(1) =
%3D
Transcribed Image Text:Let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 3, h'(1) = 4, g'(2) = 3, and f'(3) = 7. Find r'(1) %3D %3D %3D %3D %3D r'(1) = %3D
Expert Solution
Step 1

Recall:

  • The derivative of a composition is the product of the derivative of the outer function ( with the inner function is plugged in) and the derivative of the inner function.                                                                                                                               i.e, [f(g(x))]' = f'(g(x)).g'(x)
steps

Step by step

Solved in 3 steps with 2 images

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