Explanation Given: The given equation is d d x cot x = − csc 2 x Calculation: First of all express the cot x in terms of sin x and cos x as shown. d d x cot x = d d x ( cos x sin x ) { Using trigonometric identity: cot x = cos x sin x Now use the product rule and differentiate the right-side term d d x cot x = sin x ⋅ d d x cos x − cos x ⋅ d d x sin x sin 2 x { Using product rule of derivative d d x cot x = sin x ⋅ ( − sin x ) − cos x ⋅ (

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 3.3, Problem 57PS

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To Prove: Derivative of cotx is −csc2x .

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Chapter 3.3, Problem 56PS

Chapter 3.3, Problem 58PS

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Chapter 3 Solutions

Calculus

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To Prove: Derivative of cot x is − csc 2 x .

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