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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How can I find the derivative of this problem?
![Transcription:
The image contains handwritten notes including mathematical expressions. Specifically, the part transcribed here is labeled "31)" and presents the following equation:
\[ y = \frac{t e^t}{e^{2t} + 1} + 2 \]
Explanation:
The equation defines a function \( y \) in terms of the variable \( t \). The expression involves exponential functions and consists of the following components:
- The numerator of the fraction is \( t e^t \), indicating the product of \( t \) and the exponential function \( e^t \).
- The denominator is \( e^{2t} + 1 \), which is the sum of the exponential function \( e^{2t} \) and 1.
- There is an additional constant term, 2, added to the fraction.
This equation may be used in the context of calculus or differential equations as part of a larger mathematical problem or analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7893f308-81f4-4958-8f2b-4b2bd5940b5c%2F5fd4a981-a96f-4250-a10a-bdeb32d4cf20%2Fpeo4nsa.jpeg&w=3840&q=75)
Transcribed Image Text:Transcription:
The image contains handwritten notes including mathematical expressions. Specifically, the part transcribed here is labeled "31)" and presents the following equation:
\[ y = \frac{t e^t}{e^{2t} + 1} + 2 \]
Explanation:
The equation defines a function \( y \) in terms of the variable \( t \). The expression involves exponential functions and consists of the following components:
- The numerator of the fraction is \( t e^t \), indicating the product of \( t \) and the exponential function \( e^t \).
- The denominator is \( e^{2t} + 1 \), which is the sum of the exponential function \( e^{2t} \) and 1.
- There is an additional constant term, 2, added to the fraction.
This equation may be used in the context of calculus or differential equations as part of a larger mathematical problem or analysis.
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