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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![Below is the transcription of the given mathematical image, which seems to be about a multivariable function and its partial derivative. Here's how it might appear on an educational website:
---
### Multivariable Function and Partial Derivative
**Function Definition:**
\[ f(x, y) = \sqrt{2x^2 + 5y^2} \]
**Partial Derivative Calculation:**
To find the partial derivative of the function with respect to \( x \) at the point \((0,1)\):
\[ f_x(0, 1) = \_\_\_\_\_\_ \]
**Explanation:**
The given function is a multivariable function defined as:
\[ f(x, y) = \sqrt{2x^2 + 5y^2} \]
To compute the partial derivative of \( f \) with respect to \( x \), represented as \( f_x \), we take the derivative of \( f \) with \( x \) while treating \( y \) as a constant.
Then, we evaluate this derivative at the point \((0,1)\), which means substituting \( x = 0 \) and \( y = 1 \) into the derivative expression.
---
Note: Students or readers are expected to perform the differentiation and substitute the values to find \( f_x(0, 1) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F622a1a9e-da70-4332-96fa-d56b5a5adde8%2F4fc2bb92-a988-4643-b7b0-35014e046129%2Fq8gvj2b_processed.png&w=3840&q=75)
Transcribed Image Text:Below is the transcription of the given mathematical image, which seems to be about a multivariable function and its partial derivative. Here's how it might appear on an educational website:
---
### Multivariable Function and Partial Derivative
**Function Definition:**
\[ f(x, y) = \sqrt{2x^2 + 5y^2} \]
**Partial Derivative Calculation:**
To find the partial derivative of the function with respect to \( x \) at the point \((0,1)\):
\[ f_x(0, 1) = \_\_\_\_\_\_ \]
**Explanation:**
The given function is a multivariable function defined as:
\[ f(x, y) = \sqrt{2x^2 + 5y^2} \]
To compute the partial derivative of \( f \) with respect to \( x \), represented as \( f_x \), we take the derivative of \( f \) with \( x \) while treating \( y \) as a constant.
Then, we evaluate this derivative at the point \((0,1)\), which means substituting \( x = 0 \) and \( y = 1 \) into the derivative expression.
---
Note: Students or readers are expected to perform the differentiation and substitute the values to find \( f_x(0, 1) \).
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