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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![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdce9ba03-80ad-4ef0-9d01-d879c68da607%2Fecdd3a06-4103-4fb7-9cd8-d7e044f928ac%2F8yw4qwc_processed.jpeg&w=3840&q=75)
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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