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Find the derivative a) y = x sinh-(x) – Vx² + 1 b) y = cosh-(2Vx +1)

Find the derivative a) y = x sinh-(x) – Vx² + 1 b) y = cosh-(2Vx +1)

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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Question
**Problem 1: Find the Derivative** a) \( y = x \sinh^{-1}(x) - \sqrt{x^2 + 1} \) b) \( y = \cosh^{-1}(2 \sqrt{x + 1}) \) **Description:** This problem requires finding the derivative of two functions involving inverse hyperbolic functions. The expression in part (a) combines a linear term with the inverse hyperbolic sine function and a square root term. Part (b) involves the inverse hyperbolic cosine function applied to a transformed argument. To solve, apply rules for derivatives, including those for inverse hyperbolic functions, chain rule, and derivative of square roots.
Transcribed Image Text:**Problem 1: Find the Derivative** a) \( y = x \sinh^{-1}(x) - \sqrt{x^2 + 1} \) b) \( y = \cosh^{-1}(2 \sqrt{x + 1}) \) **Description:** This problem requires finding the derivative of two functions involving inverse hyperbolic functions. The expression in part (a) combines a linear term with the inverse hyperbolic sine function and a square root term. Part (b) involves the inverse hyperbolic cosine function applied to a transformed argument. To solve, apply rules for derivatives, including those for inverse hyperbolic functions, chain rule, and derivative of square roots.
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