Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![### Problem Statement:
Find the derivative \( f'(x) \).
### Function Definition:
\[ f(x) = 4e^{-3x} \]
### Solution:
To find the derivative \( f'(x) \), apply the chain rule to the exponential function. The derivative of \( e^{u} \) with respect to \( x \) where \( u \) is a function of \( x \), is \( e^{u} \times u' \).
- Given \( u = -3x \), the derivative \( u' = -3 \).
- Therefore, \( f'(x) = 4e^{-3x} \times (-3) = -12e^{-3x} \).
### Conclusion:
\[ f'(x) = \boxed{-12e^{-3x}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbbe47654-762f-4eea-844b-6a49397579c0%2Ff683f19b-9f34-48bd-ba67-15ee5e653e94%2F4ai34h_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
Find the derivative \( f'(x) \).
### Function Definition:
\[ f(x) = 4e^{-3x} \]
### Solution:
To find the derivative \( f'(x) \), apply the chain rule to the exponential function. The derivative of \( e^{u} \) with respect to \( x \) where \( u \) is a function of \( x \), is \( e^{u} \times u' \).
- Given \( u = -3x \), the derivative \( u' = -3 \).
- Therefore, \( f'(x) = 4e^{-3x} \times (-3) = -12e^{-3x} \).
### Conclusion:
\[ f'(x) = \boxed{-12e^{-3x}} \]
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