To find: use part 1 of the fundamental theorem of calculus to find the derivative of the function.
Answer to Problem 12E
The derivative of the function is
Explanation of Solution
Given information: The function is
Let’s remind of the fundamental theorem of calculus part 1:
The fundamental theorem of calculus part 1: If f is continuous on
First, we will use the properties of definite integral to match the form in fundamental theorem of calculus part 1.
So,
Hence,
Now given,
Differentiation with respect to x,
Thus,
Hence, The derivative of the function is
Chapter 5 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning