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(x) = ₁² ² sin(t) -4x 1+t2 If f(x) = -dt, then f'(x) =

(x) = ₁² ² sin(t) -4x 1+t2 If f(x) = -dt, then f'(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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Question
The image contains a mathematical expression related to calculus, specifically involving an integral and a derivative. The expression is: "If \( f(x) = \int_{1 - 4x}^{4} \frac{\sin(t)}{1 + t^2} \, dt \), then \( f'(x) = \) [blank]." This is a problem that requires finding the derivative of a function defined by an integral with variable limits. It involves using the Fundamental Theorem of Calculus, possibly Leibniz's rule for differentiation under the integral sign, to determine \( f'(x) \).
Transcribed Image Text:The image contains a mathematical expression related to calculus, specifically involving an integral and a derivative. The expression is: "If \( f(x) = \int_{1 - 4x}^{4} \frac{\sin(t)}{1 + t^2} \, dt \), then \( f'(x) = \) [blank]." This is a problem that requires finding the derivative of a function defined by an integral with variable limits. It involves using the Fundamental Theorem of Calculus, possibly Leibniz's rule for differentiation under the integral sign, to determine \( f'(x) \).
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