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
![In this exercise, we need to find the partial derivative of the expression \(4e^{4xy}\) with respect to \(x\).
### Problem Statement:
Find \(\frac{\partial}{\partial x} 4e^{4xy}\).
### Solution:
The solution provided in the box is:
\[
\frac{4e^{4xy}(4xy - 1)}{x^2}
\]
### Explanation:
To solve this problem, you would typically apply the chain rule for differentiation. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.
The original function, \(4e^{4xy}\), is an exponential function where the exponent is a function of both \(x\) and \(y\). You need to differentiate it with respect to \(x\), treating \(y\) as a constant.
### Additional Information:
- **Question Help: Video**
- It seems like there is an option to view a video for additional help on solving this type of problem. This could provide a step-by-step tutorial or explanation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4f75436-93ee-4e58-a0e3-afe0fa0e1ea5%2Fccc2ca55-c0ee-4908-8392-cd6215d15521%2Fb4j02zj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In this exercise, we need to find the partial derivative of the expression \(4e^{4xy}\) with respect to \(x\).
### Problem Statement:
Find \(\frac{\partial}{\partial x} 4e^{4xy}\).
### Solution:
The solution provided in the box is:
\[
\frac{4e^{4xy}(4xy - 1)}{x^2}
\]
### Explanation:
To solve this problem, you would typically apply the chain rule for differentiation. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.
The original function, \(4e^{4xy}\), is an exponential function where the exponent is a function of both \(x\) and \(y\). You need to differentiate it with respect to \(x\), treating \(y\) as a constant.
### Additional Information:
- **Question Help: Video**
- It seems like there is an option to view a video for additional help on solving this type of problem. This could provide a step-by-step tutorial or explanation.
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