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Which of the following is the derivative of f (g(h(x)))?

Which of the following is the derivative of f (g(h(x)))?

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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Which of the following is the derivative of \( f(g(h(x))) \)? a. \( f'(g'(h'(x))) \) b. \( f'(g(h(x))) \cdot g'(h(x)) \) c. \( f'(g(h(x))) \cdot g'(h(x)) \cdot h'(x) \) d. \( f'(g(h(x))) \cdot g'(h(x)) \cdot h'(x) \cdot x \) This question involves applying the chain rule for derivatives, where \( f \), \( g \), and \( h \) are functions, and \( f \circ g \circ h \) represents function composition. The correct application involves differentiating each function in the order of the composition.
Transcribed Image Text:Which of the following is the derivative of \( f(g(h(x))) \)? a. \( f'(g'(h'(x))) \) b. \( f'(g(h(x))) \cdot g'(h(x)) \) c. \( f'(g(h(x))) \cdot g'(h(x)) \cdot h'(x) \) d. \( f'(g(h(x))) \cdot g'(h(x)) \cdot h'(x) \cdot x \) This question involves applying the chain rule for derivatives, where \( f \), \( g \), and \( h \) are functions, and \( f \circ g \circ h \) represents function composition. The correct application involves differentiating each function in the order of the composition.
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