Differentiating Integrals Under mild continuity restrictions, it is true that if F(x) = g(t, x) dt, then F'(x) = 8,(t, x) dt. Using this fact and the Chain Rule, we can find the derivative of rf(x) F(x) g(t, x) dt by letting G(u, x) = | 8(t, x) dt, where u = f(x). Find the derivatives of the functions in Exercises 59 and 60. 59. F(x) = Vª + x³ dt 60. F(x) /ß + x² dt
Differentiating Integrals Under mild continuity restrictions, it is true that if F(x) = g(t, x) dt, then F'(x) = 8,(t, x) dt. Using this fact and the Chain Rule, we can find the derivative of rf(x) F(x) g(t, x) dt by letting G(u, x) = | 8(t, x) dt, where u = f(x). Find the derivatives of the functions in Exercises 59 and 60. 59. F(x) = Vª + x³ dt 60. F(x) /ß + x² dt
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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