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Calculate the derivative a s In (t)dt using Part 2 of the Fundamental Theorem of Calculus. Enclose arguments of functions in parentheses. For example, sin (2æ). d dz In (t)dt =

Calculate the derivative a s In (t)dt using Part 2 of the Fundamental Theorem of Calculus. Enclose arguments of functions in parentheses. For example, sin (2æ). d dz In (t)dt =

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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Calculate the derivative:

 

Enclose arguments of functions in parentheses. 

### Calculating Derivatives Using the Fundamental Theorem of Calculus This section aims to illustrate the process of calculating the derivative of an integral expression using Part 2 of the Fundamental Theorem of Calculus. Consider the following expression for which we need to calculate the derivative: \[ \frac{d}{dx} \int_{x^8}^{e^{5x}} \ln(t) \, dt \] **Note:** Enclose arguments of functions in parentheses. For example, \(\sin(2x)\). Using Part 2 of the Fundamental Theorem of Calculus, compute the derivative as follows: \[ \frac{d}{dx} \int_{x^8}^{e^{5x}} \ln(t) \, dt = \] (A blank box is provided for the answer along with copy and paste icons for efficient use.) This problem can be solved by applying the Leibniz rule for differentiation under the integral sign, taking into account both bounds of the integral.
Transcribed Image Text:### Calculating Derivatives Using the Fundamental Theorem of Calculus This section aims to illustrate the process of calculating the derivative of an integral expression using Part 2 of the Fundamental Theorem of Calculus. Consider the following expression for which we need to calculate the derivative: \[ \frac{d}{dx} \int_{x^8}^{e^{5x}} \ln(t) \, dt \] **Note:** Enclose arguments of functions in parentheses. For example, \(\sin(2x)\). Using Part 2 of the Fundamental Theorem of Calculus, compute the derivative as follows: \[ \frac{d}{dx} \int_{x^8}^{e^{5x}} \ln(t) \, dt = \] (A blank box is provided for the answer along with copy and paste icons for efficient use.) This problem can be solved by applying the Leibniz rule for differentiation under the integral sign, taking into account both bounds of the integral.
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