Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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**Find the derivative of the function.** \[ y = \tan^{-1} \left( \frac{x}{a} \right) + \ln \left( \sqrt{\frac{x+a}{x-a}} \right) \] \[ y' = \text{______} \] **Explanation**: The task requires finding the derivative \( y' \) of the given function \( y \). The function is a combination of an inverse tangent function and a natural logarithm of a square root expression. To differentiate this function, apply the chain rule, the derivative rules for inverse trigonometric functions, and the derivative rules for logarithms.
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Transcribed Image Text:**Find the derivative of the function.** \[ y = \tan^{-1} \left( \frac{x}{a} \right) + \ln \left( \sqrt{\frac{x+a}{x-a}} \right) \] \[ y' = \text{______} \] **Explanation**: The task requires finding the derivative \( y' \) of the given function \( y \). The function is a combination of an inverse tangent function and a natural logarithm of a square root expression. To differentiate this function, apply the chain rule, the derivative rules for inverse trigonometric functions, and the derivative rules for logarithms.
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