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...
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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)
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r'(1) =
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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)
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