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 1
**Objective**: Find \( f'(x) \).
Given:
\[ f(x) = \ln(6x^2 + 5) \]
Solution:
\[ f'(x) = \underline{\quad\quad\quad} \]
---
### Problem 2
**Objective**: Find \( f'(x) \).
Given:
\[ f(x) = \frac{1}{x^{14}} \]
Solution:
\[ f'(x) = \underline{\quad\quad\quad} \]
---
### Problem 3
**Objective**: Find \( f'(x) \).
Given:
\[ f(x) = \frac{7}{x^5} + 7\sqrt{x} \]
Solution:
\[ f'(x) = \underline{\quad\quad\quad} \]
---
### Problem 4
**Objective**: Find \( f'(x) \).
Given:
\[ f(x) = 2x^{1/2} + \frac{4}{x} + \frac{3x}{x^{2/3}} - \frac{7}{x} \]
Solution:
\[ f'(x) = \underline{\quad\quad\quad} \]
---
These problems involve finding the derivative of various functions using rules of differentiation such as the power rule and the chain rule.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb85c101b-d3f5-410c-a5d1-ffd9e9de2493%2F76eea959-c7eb-4408-84d6-4238aca0467c%2Fttj3erj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 1
**Objective**: Find \( f'(x) \).
Given:
\[ f(x) = \ln(6x^2 + 5) \]
Solution:
\[ f'(x) = \underline{\quad\quad\quad} \]
---
### Problem 2
**Objective**: Find \( f'(x) \).
Given:
\[ f(x) = \frac{1}{x^{14}} \]
Solution:
\[ f'(x) = \underline{\quad\quad\quad} \]
---
### Problem 3
**Objective**: Find \( f'(x) \).
Given:
\[ f(x) = \frac{7}{x^5} + 7\sqrt{x} \]
Solution:
\[ f'(x) = \underline{\quad\quad\quad} \]
---
### Problem 4
**Objective**: Find \( f'(x) \).
Given:
\[ f(x) = 2x^{1/2} + \frac{4}{x} + \frac{3x}{x^{2/3}} - \frac{7}{x} \]
Solution:
\[ f'(x) = \underline{\quad\quad\quad} \]
---
These problems involve finding the derivative of various functions using rules of differentiation such as the power rule and the chain rule.
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