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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![### Calculus Problem Set
#### Question 2: Simplify the function, then find the derivative.
Given the function:
\[ f(x) = \ln \left( x \sqrt{x^2 - 1} \right) \]
##### Steps:
1. **Simplify the Function:**
- Express the function in a simplified form before finding its derivative. In this case, recognize products inside the logarithm to use logarithm properties for simplification.
2. **Differentiate:**
- After simplification, use appropriate differentiation rules such as the chain rule, product rule, and logarithm differentiation rule.
Complete the derivation step by step for clarity and proper understanding.
---
(Note: In educational material, it is important to provide hints, guided steps, and detailed theory to help students understand the concepts systematically.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52db8ee6-33d1-4aac-bbe4-ebc771de1e49%2F8ca40a98-82bb-4b5d-807b-d72abde1b917%2F55kcpfj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculus Problem Set
#### Question 2: Simplify the function, then find the derivative.
Given the function:
\[ f(x) = \ln \left( x \sqrt{x^2 - 1} \right) \]
##### Steps:
1. **Simplify the Function:**
- Express the function in a simplified form before finding its derivative. In this case, recognize products inside the logarithm to use logarithm properties for simplification.
2. **Differentiate:**
- After simplification, use appropriate differentiation rules such as the chain rule, product rule, and logarithm differentiation rule.
Complete the derivation step by step for clarity and proper understanding.
---
(Note: In educational material, it is important to provide hints, guided steps, and detailed theory to help students understand the concepts systematically.)
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