Find the derivative of y with respect to x. (Hint: chain rule) y = -csc-1 24 V(8x + 92 - 9 24 (8x + 9N(8x + 9)2 - 9 -24 (8x + 9N(8x + 9)2 - 1 -24 1+ (8x + 9)2
Find the derivative of y with respect to x. (Hint: chain rule) y = -csc-1 24 V(8x + 92 - 9 24 (8x + 9N(8x + 9)2 - 9 -24 (8x + 9N(8x + 9)2 - 1 -24 1+ (8x + 9)2
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 \( y \) 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)
\[ \frac{-24}{1 + (8x + 9)^2} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F346b36e0-a4d8-47d7-8bd1-1ad776cb1cf3%2F1393af32-24c0-49b2-bd8b-997c87ba1830%2Ffheevme_processed.png&w=3840&q=75)
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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