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 Statement:**
Find the derivative of the function.
\[ y = (5x - 1)^4 (8x^2 - 1)^{-3} \]
**Solution:**
The derivative of the function is given by:
\[ y' = \frac{20(5x - 1)^3}{(8x^2 - 1)^3} - \frac{48(5x - 1)^4}{(8x^2 - 1)^4} \]
**Explanation:**
- The expression involves the use of both the product and chain rules to differentiate.
- Each term in the derivative is derived by differentiating components of the original expression.
**Note:**
Ensure to apply the power rule and chain rule correctly while differentiating each part of the expression.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f0872d9-789a-4df5-8618-3645da6a4c0b%2F696e8ac2-73b6-48dc-ab0c-73079f35aa3f%2Feu64xz9_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the derivative of the function.
\[ y = (5x - 1)^4 (8x^2 - 1)^{-3} \]
**Solution:**
The derivative of the function is given by:
\[ y' = \frac{20(5x - 1)^3}{(8x^2 - 1)^3} - \frac{48(5x - 1)^4}{(8x^2 - 1)^4} \]
**Explanation:**
- The expression involves the use of both the product and chain rules to differentiate.
- Each term in the derivative is derived by differentiating components of the original expression.
**Note:**
Ensure to apply the power rule and chain rule correctly while differentiating each part of the expression.
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