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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Find ∂f/∂x and ∂f/∂y for the following functions.
![The image contains three mathematical functions of two variables, \( x \) and \( y \).
1. The first function is:
\[
f(x, y) = x^4 - 5xy - 2y^2
\]
This is a polynomial equation involving both \( x \) and \( y \).
2. The second function is:
\[
f(x, y) = \sqrt{5x^2 + 2y^2}
\]
This represents a square root function with the expression under the square root sign involving both \( x \) squared and \( y \) squared.
3. The third function is:
\[
f(x, y) = e^{3xy} \ln(6y)
\]
This function involves an exponential term \( e^{3xy} \) and a natural logarithm \( \ln(6y) \).
Each function explores different mathematical operations applied to the variables \( x \) and \( y \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbfc23d67-2878-46d3-b2ec-822f6f1a78a5%2F4fb7627b-479a-4d84-8477-eb506260c28a%2Fe9uw9y_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains three mathematical functions of two variables, \( x \) and \( y \).
1. The first function is:
\[
f(x, y) = x^4 - 5xy - 2y^2
\]
This is a polynomial equation involving both \( x \) and \( y \).
2. The second function is:
\[
f(x, y) = \sqrt{5x^2 + 2y^2}
\]
This represents a square root function with the expression under the square root sign involving both \( x \) squared and \( y \) squared.
3. The third function is:
\[
f(x, y) = e^{3xy} \ln(6y)
\]
This function involves an exponential term \( e^{3xy} \) and a natural logarithm \( \ln(6y) \).
Each function explores different mathematical operations applied to the variables \( x \) and \( y \).
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