Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question

This uses quotient rule

Differentiate. Given the function: \[ f(\theta) = \frac{\sin(\theta)}{1 + \cos(\theta)} \] The derivative \( f'(\theta) \) is calculated as: \[ f'(\theta) = \frac{(1 + \cos(\theta)) \cos(\theta) - \sin(\theta)(-\sin(\theta))}{(1 + \cos(\theta))^2} \]
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Transcribed Image Text:Differentiate. Given the function: \[ f(\theta) = \frac{\sin(\theta)}{1 + \cos(\theta)} \] The derivative \( f'(\theta) \) is calculated as: \[ f'(\theta) = \frac{(1 + \cos(\theta)) \cos(\theta) - \sin(\theta)(-\sin(\theta))}{(1 + \cos(\theta))^2} \]
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Step 1: Quotient Rule of differentiation :
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Step 2: To differentiate:
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