Let f(x) - 6 cos 6 cos° x f '(x) =

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.
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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