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: Differentiation Problems
#### Problem Set
**34. Find \( f'(x) \).**
Given:
\[ f(x) = \frac{8x^2 + 1}{x^2 + 8} \]
Find:
\[ f'(x) = \underline{\hspace{5cm}} \]
---
**35. Find \( f'(x) \).**
Given:
\[ f(x) = 2x \, e^x \]
Find:
\[ f'(x) = \underline{\hspace{5cm}} \]
---
**36. Find \( f'(x) \).**
Given:
\[ f(x) = 7e^{-3x} \]
Find:
\[ f'(x) = \underline{\hspace{5cm}} \]
---
**37. Find \( f'(x) \).**
Given:
\[ f(x) = (2 + \ln x)^8 \]
Find:
\[ f'(x) = \underline{\hspace{5cm}} \]
---
**38. Find \( f'(x) \).**
Given:
\[ f(x) = \sqrt{x^2 + 6} \]
Find:
\[ f'(x) = \underline{\hspace{5cm}} \]
---
**39. Find \( f'(x) \).**
Given:
\[ f(x) = 3x \, e^{8x} \]
Find:
\[ f'(x) = \underline{\hspace{5cm}} \]
---
**Note:** These exercises focus on differentiating a range of functions, including polynomial, exponential, and logarithmic forms. Please apply the relevant differentiation rules, such as the product rule, quotient rule, chain rule, and natural log derivatives, where appropriate.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb85c101b-d3f5-410c-a5d1-ffd9e9de2493%2F89b7a585-2b99-465f-a334-5c0dededc283%2F3cdm7xk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Below is a transcription of the text from the image, formatted for an educational website:
---
### Calculus: Differentiation Problems
#### Problem Set
**34. Find \( f'(x) \).**
Given:
\[ f(x) = \frac{8x^2 + 1}{x^2 + 8} \]
Find:
\[ f'(x) = \underline{\hspace{5cm}} \]
---
**35. Find \( f'(x) \).**
Given:
\[ f(x) = 2x \, e^x \]
Find:
\[ f'(x) = \underline{\hspace{5cm}} \]
---
**36. Find \( f'(x) \).**
Given:
\[ f(x) = 7e^{-3x} \]
Find:
\[ f'(x) = \underline{\hspace{5cm}} \]
---
**37. Find \( f'(x) \).**
Given:
\[ f(x) = (2 + \ln x)^8 \]
Find:
\[ f'(x) = \underline{\hspace{5cm}} \]
---
**38. Find \( f'(x) \).**
Given:
\[ f(x) = \sqrt{x^2 + 6} \]
Find:
\[ f'(x) = \underline{\hspace{5cm}} \]
---
**39. Find \( f'(x) \).**
Given:
\[ f(x) = 3x \, e^{8x} \]
Find:
\[ f'(x) = \underline{\hspace{5cm}} \]
---
**Note:** These exercises focus on differentiating a range of functions, including polynomial, exponential, and logarithmic forms. Please apply the relevant differentiation rules, such as the product rule, quotient rule, chain rule, and natural log derivatives, where appropriate.
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