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Given f(x, y) = 2a° + 5æ?y – 3y?, find %3D f-(x, y) = %D f,(x, y) = %3D fza (t, y) = %3D fzy(t, y) = %3D

Given f(x, y) = 2a° + 5æ?y – 3y?, find %3D f-(x, y) = %D f,(x, y) = %3D fza (t, y) = %3D fzy(t, y) = %3D

Calculus: Early Transcendentals
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:** Given \( f(x, y) = 2x^6 + 5x^2y^5 - 3y^2 \), find: 1. \( f_x(x, y) = \) _____ 2. \( f_y(x, y) = \) _____ 3. \( f_{xx}(x, y) = \) _____ 4. \( f_{xy}(x, y) = \) _____ **Explanation:** This problem involves finding the partial derivatives of the function \( f(x, y) \). - \( f_x(x, y) \) is the partial derivative of \( f \) with respect to \( x \). - \( f_y(x, y) \) is the partial derivative of \( f \) with respect to \( y \). - \( f_{xx}(x, y) \) is the second partial derivative of \( f \) with respect to \( x \). - \( f_{xy}(x, y) \) is the mixed partial derivative, first with respect to \( x \) and then \( y \). To solve, you must apply rules for differentiation, treating other variables as constants during each step accordingly.
Transcribed Image Text:**Problem Statement:** Given \( f(x, y) = 2x^6 + 5x^2y^5 - 3y^2 \), find: 1. \( f_x(x, y) = \) _____ 2. \( f_y(x, y) = \) _____ 3. \( f_{xx}(x, y) = \) _____ 4. \( f_{xy}(x, y) = \) _____ **Explanation:** This problem involves finding the partial derivatives of the function \( f(x, y) \). - \( f_x(x, y) \) is the partial derivative of \( f \) with respect to \( x \). - \( f_y(x, y) \) is the partial derivative of \( f \) with respect to \( y \). - \( f_{xx}(x, y) \) is the second partial derivative of \( f \) with respect to \( x \). - \( f_{xy}(x, y) \) is the mixed partial derivative, first with respect to \( x \) and then \( y \). To solve, you must apply rules for differentiation, treating other variables as constants during each step accordingly.
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