21. Find f'(x) for f(x) = 6x e 6x %3D f'(x) = 22. Find f'(x) for f(x) = In (5 –7x) %3D f'(x) = 23. Find f'(x) for f(x) = In (3x) f'(x) = 24. Find f'(x) for f(x) = 7In(7x). f'(x) = %3D 25. Find f'(x) for f(x)= 2x In(2x).
21. Find f'(x) for f(x) = 6x e 6x %3D f'(x) = 22. Find f'(x) for f(x) = In (5 –7x) %3D f'(x) = 23. Find f'(x) for f(x) = In (3x) f'(x) = 24. Find f'(x) for f(x) = 7In(7x). f'(x) = %3D 25. Find f'(x) for f(x)= 2x In(2x).
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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![Here is the transcription of the image content for an educational context:
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### Calculus: Differentiation Exercises
**21.** Find \( f'(x) \) for \( f(x) = 6x \cdot e^{6x} \)
\[ f'(x) = \underline{\hspace{3cm}} \]
**22.** Find \( f'(x) \) for \( f(x) = \ln(5 - 7x) \)
\[ f'(x) = \underline{\hspace{3cm}} \]
**23.** Find \( f'(x) \) for \( f(x) = \ln(3x) \)
\[ f'(x) = \underline{\hspace{3cm}} \]
**24.** Find \( f'(x) \) for \( f(x) = 7\ln(7x) \)
\[ f'(x) = \underline{\hspace{3cm}} \]
**25.** Find \( f'(x) \) for \( f(x) = 2x \ln(2x) \)
\[ f'(x) = \underline{\hspace{3cm}} \]
---
These exercises involve finding the derivative of various functions involving exponential and logarithmic expressions. Use differentiation rules like the product rule and chain rule to solve these problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb85c101b-d3f5-410c-a5d1-ffd9e9de2493%2Fe84b4480-14cc-4f20-b701-bedd32c2a783%2F2z763bg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Here is the transcription of the image content for an educational context:
---
### Calculus: Differentiation Exercises
**21.** Find \( f'(x) \) for \( f(x) = 6x \cdot e^{6x} \)
\[ f'(x) = \underline{\hspace{3cm}} \]
**22.** Find \( f'(x) \) for \( f(x) = \ln(5 - 7x) \)
\[ f'(x) = \underline{\hspace{3cm}} \]
**23.** Find \( f'(x) \) for \( f(x) = \ln(3x) \)
\[ f'(x) = \underline{\hspace{3cm}} \]
**24.** Find \( f'(x) \) for \( f(x) = 7\ln(7x) \)
\[ f'(x) = \underline{\hspace{3cm}} \]
**25.** Find \( f'(x) \) for \( f(x) = 2x \ln(2x) \)
\[ f'(x) = \underline{\hspace{3cm}} \]
---
These exercises involve finding the derivative of various functions involving exponential and logarithmic expressions. Use differentiation rules like the product rule and chain rule to solve these problems.
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