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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![Let
\( f(x) = -6 \cos^5 x \)
\[ f'(x) = \]
The expression is asking for the derivative of the function \( f(x) = -6 \cos^5 x \).
### Explanation:
- The function \( f(x) \) involves the cosine function raised to the fifth power, multiplied by \(-6\).
- To find \( f'(x) \), apply the chain rule for differentiation:
- Differentiate the outer function: if \( u = \cos x \), then \((u^5)' = 5u^4\).
- Multiply by the derivative of the inner function \( u = \cos x \), which is \(-\sin x\).
- So, plugging in, \( f'(x) \) involves these steps combined.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd64ca58-ec83-4992-8af5-b821b66a4328%2F38debacf-d6a6-4445-a0aa-c806e15f0c9d%2Fvy3ft4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let
\( f(x) = -6 \cos^5 x \)
\[ f'(x) = \]
The expression is asking for the derivative of the function \( f(x) = -6 \cos^5 x \).
### Explanation:
- The function \( f(x) \) involves the cosine function raised to the fifth power, multiplied by \(-6\).
- To find \( f'(x) \), apply the chain rule for differentiation:
- Differentiate the outer function: if \( u = \cos x \), then \((u^5)' = 5u^4\).
- Multiply by the derivative of the inner function \( u = \cos x \), which is \(-\sin x\).
- So, plugging in, \( f'(x) \) involves these steps combined.
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