Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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**Find the derivative of \( y \) with respect to \( x \). (Hint: chain rule)** Given: \[ y = -\csc^{-1}\left( \frac{8x + 9}{3} \right) \] Options for the derivative: A) \[ \frac{24}{\sqrt{(8x + 9)^2 - 9}} \] B) \[ \frac{24}{(8x + 9)\sqrt{(8x + 9)^2 - 9}} \] C) \[ \frac{-24}{(8x + 9)\sqrt{(8x + 9)^2 - 1}} \] D) \[ \frac{-24}{1 + (8x + 9)^2} \]
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Transcribed Image Text:**Find the derivative of \( y \) with respect to \( x \). (Hint: chain rule)** Given: \[ y = -\csc^{-1}\left( \frac{8x + 9}{3} \right) \] Options for the derivative: A) \[ \frac{24}{\sqrt{(8x + 9)^2 - 9}} \] B) \[ \frac{24}{(8x + 9)\sqrt{(8x + 9)^2 - 9}} \] C) \[ \frac{-24}{(8x + 9)\sqrt{(8x + 9)^2 - 1}} \] D) \[ \frac{-24}{1 + (8x + 9)^2} \]
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