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If f(x) f'(x) = f'(1) = 2 sin x 3 + cos x 2(1+3 cos(x)) (3 + cos(x))² then

If f(x) f'(x) = f'(1) = 2 sin x 3 + cos x 2(1+3 cos(x)) (3 + cos(x))² then

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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The image contains a mathematical problem related to derivatives, which is appropriate for an educational context, such as a calculus lesson. The problem is stated as follows: If \( f(x) = \frac{2 \sin x}{3 + \cos x} \), then \[ f'(x) = \frac{2(1 + 3 \cos(x))}{(3 + \cos(x))^2} \] There is a checkmark icon next to this expression, indicating that this is the correct derivative. The problem continues with a blank space for: \[ f'(1) = \] This implies that the next step is to evaluate the derivative at \( x = 1 \). The expression is set up as a quotient rule problem in calculus, where the derivative of the function \( f(x) \) is provided, and the next task is to compute its value at \( x = 1 \).
Transcribed Image Text:The image contains a mathematical problem related to derivatives, which is appropriate for an educational context, such as a calculus lesson. The problem is stated as follows: If \( f(x) = \frac{2 \sin x}{3 + \cos x} \), then \[ f'(x) = \frac{2(1 + 3 \cos(x))}{(3 + \cos(x))^2} \] There is a checkmark icon next to this expression, indicating that this is the correct derivative. The problem continues with a blank space for: \[ f'(1) = \] This implies that the next step is to evaluate the derivative at \( x = 1 \). The expression is set up as a quotient rule problem in calculus, where the derivative of the function \( f(x) \) is provided, and the next task is to compute its value at \( x = 1 \).
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