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Find fx (x,y) and f, (x,y). Then find fx (2, -1) and fy(-4,3). f(x,y)= ex+y+5 fx(x,y)=

Find fx (x,y) and f, (x,y). Then find fx (2, -1) and fy(-4,3). f(x,y)= ex+y+5 fx(x,y)=

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 39RE
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Title: Partial Derivatives and Evaluation --- **Finding Partial Derivatives: \( f_x(x, y) \) and \( f_y(x, y) \)** Task: Determine \( f_x(x, y) \) and \( f_y(x, y) \). Subsequently, calculate \( f_x(2, -1) \) and \( f_y(-4, 3) \). Given the function: \[ f(x, y) = e^{x + y} + 5 \] ### Instructions: 1. **Compute \( f_x(x, y) \)**: The partial derivative of \( f \) with respect to \( x \). 2. **Compute \( f_y(x, y) \)**: The partial derivative of \( f \) with respect to \( y \). 3. **Evaluate**: - \( f_x(2, -1) \) - \( f_y(-4, 3) \) --- ### Solution: - **Partial Derivative with respect to \( x \)**: \[ f_x(x, y) = \] (Students should solve and input their steps and conclusions here.) ### Graphs/Diagrams: - (If applicable, explain the graphical representation of partial derivatives or approaches to visualize this function.) --- *Note: Be sure to double-check your steps and understand the relationship between the function variables and their partial derivatives for thorough comprehension.* --- For additional resources and explanations, please refer to our calculus section or contact the educational support team.
Transcribed Image Text:Title: Partial Derivatives and Evaluation --- **Finding Partial Derivatives: \( f_x(x, y) \) and \( f_y(x, y) \)** Task: Determine \( f_x(x, y) \) and \( f_y(x, y) \). Subsequently, calculate \( f_x(2, -1) \) and \( f_y(-4, 3) \). Given the function: \[ f(x, y) = e^{x + y} + 5 \] ### Instructions: 1. **Compute \( f_x(x, y) \)**: The partial derivative of \( f \) with respect to \( x \). 2. **Compute \( f_y(x, y) \)**: The partial derivative of \( f \) with respect to \( y \). 3. **Evaluate**: - \( f_x(2, -1) \) - \( f_y(-4, 3) \) --- ### Solution: - **Partial Derivative with respect to \( x \)**: \[ f_x(x, y) = \] (Students should solve and input their steps and conclusions here.) ### Graphs/Diagrams: - (If applicable, explain the graphical representation of partial derivatives or approaches to visualize this function.) --- *Note: Be sure to double-check your steps and understand the relationship between the function variables and their partial derivatives for thorough comprehension.* --- For additional resources and explanations, please refer to our calculus section or contact the educational support team.
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