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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Question
![**Problem Statement:**
Find the derivative of the function.
\[ y = e^k \tan(\sqrt{5x}) \]
\[ y'(x) = \]
**Instructions:**
To solve this problem, you'll need to apply the chain rule and the derivative of the tangent function. Remember that:
- The derivative of \( \tan(u) \) is \( \sec^2(u) \cdot u' \).
- The derivative of \( \sqrt{5x} \) is \( \frac{1}{2\sqrt{5x}} \cdot 5 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F502f3db3-ecd6-441f-bb50-2cf395b97b8e%2F536d8c97-10be-4fc0-9fd5-a971838499fb%2F9wj19w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the derivative of the function.
\[ y = e^k \tan(\sqrt{5x}) \]
\[ y'(x) = \]
**Instructions:**
To solve this problem, you'll need to apply the chain rule and the derivative of the tangent function. Remember that:
- The derivative of \( \tan(u) \) is \( \sec^2(u) \cdot u' \).
- The derivative of \( \sqrt{5x} \) is \( \frac{1}{2\sqrt{5x}} \cdot 5 \).
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