The functions ƒ and g are differentiable and h(x) = f(g(x)). Use the information below to find h' (2).f(2) = -1f' (2) = 3f'(1) = 4g'(2) = -19(-6) — 6 д'(-6) — —3f(1) = -6g(2)1а) О4b) O-8c) 00d) O1e) О-4

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Answered: The functions f and g are…

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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Find the derivative for each and use proper notation and simplify what needed
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The graphs of f and g are shown. Let h(x) = f(g(x)) and s(x) = g(f(x)). y 15 10 5 -2 4 6. 10 (a) Write an equation for h'(x) in terms of f(x), g(x), f'(x), and g'(x). O h'(x) = g'(f'(x))f'(x) O h'(x) = g'(f(x))f'(x) h'(x) = f'(g'(x))g'(x) h'(x) = f'(g(x))gʻ(x) O h'(x) = f'(g'(x))g(x) O h'(x) = g'(f'(x))f(x) Find h'(3). (If an answer does not exist, enter DNE.) (b) Write an equation for s'(x) in terms of f(x), g(x), f'(x), and g'(x). O s'(x) = f'(g(x))g'(x) O s'(x) = g'(f'(x))F'(x) O s'(x) = f'(g'(x))g'(x) s'(x) = g'(f(x))f'(x) s'(x) = f'(g'(x))g(x) s'(x) = g'(f'(x)){x) Find s'(7). (If an answer does not exist, enter DNE.)
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The functions f and g are differentiable and h(x) = f(9(x)). Use the information below to find h'(2). f(2) = -1 f(1) = -6 g(2) = 1 g(-6) = 6 g'(-–6) = -3 f'(2) = 3 f'(1) = 4 g'(2) = -1 а) О4 b) O-8 c) 00 d) O1