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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![(a) Find the derivative.
\[ y = \frac{1}{3} \ln(x^2 - 6) \]
\[ \frac{dy}{dx} = \_\_\_\_\_ \]
(b) Find the derivative.
\[ y = \ln\left(\sqrt[3]{x^2 - 6}\right) \]
\[ \frac{dy}{dx} = \_\_\_\_\_ \]
### Explanation:
The problem presents two expressions for which we need to find derivatives. There are no graphs or diagrams in the image, only mathematical expressions. The expressions involve logarithmic and polynomial functions, and their derivatives will require application of differentiation rules, including the chain rule and properties of logarithms.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F246f6db2-1dc3-454a-8242-1f5f62a81278%2Fe66afaf1-6684-475c-b2a2-ba4f2c978a71%2F66q73xo_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Find the derivative.
\[ y = \frac{1}{3} \ln(x^2 - 6) \]
\[ \frac{dy}{dx} = \_\_\_\_\_ \]
(b) Find the derivative.
\[ y = \ln\left(\sqrt[3]{x^2 - 6}\right) \]
\[ \frac{dy}{dx} = \_\_\_\_\_ \]
### Explanation:
The problem presents two expressions for which we need to find derivatives. There are no graphs or diagrams in the image, only mathematical expressions. The expressions involve logarithmic and polynomial functions, and their derivatives will require application of differentiation rules, including the chain rule and properties of logarithms.
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