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f., f, and f_, and evaluate each at the given point. x'y ху f(x, у, 2) 3- (4, 1, –1) x + y + z fx(X, y, z) fy(x, y, z) f_(x, y, z) %D f,(4, 1, –1) = fy(4, 1, -1) f(4, 1, -1) = %3D

f., f, and f_, and evaluate each at the given point. x'y ху f(x, у, 2) 3- (4, 1, –1) x + y + z fx(X, y, z) fy(x, y, z) f_(x, y, z) %D f,(4, 1, –1) = fy(4, 1, -1) f(4, 1, -1) = %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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**Problem Statement:** Find the partial derivatives \( f_x', f_y', \) and \( f_z' \), and evaluate each at the given point. **Function Definition:** \[ f(x, y, z) = \frac{xy}{x + y + z}, \quad (4, 1, -1) \] **Required Partial Derivatives:** 1. \( f_x(x, y, z) = \) [Enter the expression here] 2. \( f_y(x, y, z) = \) [Enter the expression here] 3. \( f_z(x, y, z) = \) [Enter the expression here] **Evaluate Partial Derivatives at the Point (4, 1, -1):** 1. \( f_x(4, 1, -1) = \) [Enter the value here] 2. \( f_y(4, 1, -1) = \) [Enter the value here] 3. \( f_z(4, 1, -1) = \) [Enter the value here] **Instructions:** - Find the partial derivatives by applying the rules of differentiation. - Substitute the point \( (4, 1, -1) \) into the derived expressions to find the evaluated values. This exercise involves finding and evaluating partial derivatives of a given multivariable function at a specific point.
Transcribed Image Text:**Problem Statement:** Find the partial derivatives \( f_x', f_y', \) and \( f_z' \), and evaluate each at the given point. **Function Definition:** \[ f(x, y, z) = \frac{xy}{x + y + z}, \quad (4, 1, -1) \] **Required Partial Derivatives:** 1. \( f_x(x, y, z) = \) [Enter the expression here] 2. \( f_y(x, y, z) = \) [Enter the expression here] 3. \( f_z(x, y, z) = \) [Enter the expression here] **Evaluate Partial Derivatives at the Point (4, 1, -1):** 1. \( f_x(4, 1, -1) = \) [Enter the value here] 2. \( f_y(4, 1, -1) = \) [Enter the value here] 3. \( f_z(4, 1, -1) = \) [Enter the value here] **Instructions:** - Find the partial derivatives by applying the rules of differentiation. - Substitute the point \( (4, 1, -1) \) into the derived expressions to find the evaluated values. This exercise involves finding and evaluating partial derivatives of a given multivariable function at a specific point.
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