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(a) Given F(2) 3, F'(2) 4, F(4) 1, F'(4) = 5 and G(1) 3, G'(1) %3D 4, G(4) = 2, G'(4) = 7, find each of the following. %3D %3D i. H(4) if H(x) = F(G(x)) ii. H'(4) if H(x) = F(G(x)) iii. H(4) if H(x) = G(F(x)) %3D %3D %3D

(a) Given F(2) 3, F'(2) 4, F(4) 1, F'(4) = 5 and G(1) 3, G'(1) %3D 4, G(4) = 2, G'(4) = 7, find each of the following. %3D %3D i. H(4) if H(x) = F(G(x)) ii. H'(4) if H(x) = F(G(x)) iii. H(4) if H(x) = G(F(x)) %3D %3D %3D

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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(a) Given \( F(2) = 3, F'(2) = 4, F(4) = 1, F'(4) = 5 \) and \( G(1) = 3, G'(1) = 4, G(4) = 2, G'(4) = 7 \), find each of the following. i. \( H'(4) \) if \( H(x) = F(G(x)) \) ii. \( H'(4) \) if \( H(x) = F(x)G(x) \) iii. \( H'(4) \) if \( H(x) = G(F(x)) \) iv. \( H'(4) \) if \( H(x) = G(F(x)) \) v. \( H'(4) \) if \( H(x) = \frac{F(x)}{G(x)} \) (b) Differentiate \( h(y) = \frac{\tan(10y)}{e^{(4y)} + 1} \) (c) Differentiate \( y = \sqrt{\sec^3{(5t^2)}} \) (d) Differentiate \( g(v) = \ln\left(\frac{\arctan(3v)}{\arcsin(7v) + v^2}\right) \)
Transcribed Image Text:(a) Given \( F(2) = 3, F'(2) = 4, F(4) = 1, F'(4) = 5 \) and \( G(1) = 3, G'(1) = 4, G(4) = 2, G'(4) = 7 \), find each of the following. i. \( H'(4) \) if \( H(x) = F(G(x)) \) ii. \( H'(4) \) if \( H(x) = F(x)G(x) \) iii. \( H'(4) \) if \( H(x) = G(F(x)) \) iv. \( H'(4) \) if \( H(x) = G(F(x)) \) v. \( H'(4) \) if \( H(x) = \frac{F(x)}{G(x)} \) (b) Differentiate \( h(y) = \frac{\tan(10y)}{e^{(4y)} + 1} \) (c) Differentiate \( y = \sqrt{\sec^3{(5t^2)}} \) (d) Differentiate \( g(v) = \ln\left(\frac{\arctan(3v)}{\arcsin(7v) + v^2}\right) \)
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