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Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) = e5t2 - %3D 4t dt g'(x) =

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) = e5t2 - %3D 4t dt g'(x) =

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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**Instruction:** Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. **Given Function:** \[ g(x) = \int_{2}^{x} e^{5t^2 - 4t} \, dt \] **Task:** Determine \( g'(x) \). **Explanation:** According to Part 1 of the Fundamental Theorem of Calculus, if \( g(x) = \int_{a}^{x} f(t) \, dt \), then \( g'(x) = f(x) \), provided \( f \) is continuous. This means the derivative of the function \( g(x) \) is the integrand evaluated at \( x \).
Transcribed Image Text:**Instruction:** Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. **Given Function:** \[ g(x) = \int_{2}^{x} e^{5t^2 - 4t} \, dt \] **Task:** Determine \( g'(x) \). **Explanation:** According to Part 1 of the Fundamental Theorem of Calculus, if \( g(x) = \int_{a}^{x} f(t) \, dt \), then \( g'(x) = f(x) \), provided \( f \) is continuous. This means the derivative of the function \( g(x) \) is the integrand evaluated at \( x \).
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