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b) Find the derivative of ľ 1 et In ydy.

b) Find the derivative of ľ 1 et In ydy.

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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**b) Find the derivative of \(\int_{1}^{e^{x}} \ln y \, dy\).** This question involves finding the derivative of a definite integral with a variable upper limit of integration. To solve this, you can use the Fundamental Theorem of Calculus, which states that if \( F(x) = \int_{a}^{g(x)} f(t) \, dt \), and \( f \) is continuous, then \( F'(x) = f(g(x)) \cdot g'(x) \). Therefore, you will: 1. Identify the function \( f(y) = \ln y \). 2. Use the Fundamental Theorem of Calculus to differentiate, taking into account the chain rule for the upper limit \( e^x \).
Transcribed Image Text:**b) Find the derivative of \(\int_{1}^{e^{x}} \ln y \, dy\).** This question involves finding the derivative of a definite integral with a variable upper limit of integration. To solve this, you can use the Fundamental Theorem of Calculus, which states that if \( F(x) = \int_{a}^{g(x)} f(t) \, dt \), and \( f \) is continuous, then \( F'(x) = f(g(x)) \cdot g'(x) \). Therefore, you will: 1. Identify the function \( f(y) = \ln y \). 2. Use the Fundamental Theorem of Calculus to differentiate, taking into account the chain rule for the upper limit \( e^x \).
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