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4. §13.3. Q49. Consider function w=w(x, y, z). (a). Find Ow/dx. (b). Find Ow/ay. (c). Find əw/az. w = √√√x² + y² + 2².

4. §13.3. Q49. Consider function w=w(x, y, z). (a). Find Ow/dx. (b). Find Ow/ay. (c). Find əw/az. w = √√√x² + y² + 2².

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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Show full answers to part a) b) & c)
**Title: Calculating Partial Derivatives of a Multivariable Function** --- **Section 4: Derivatives of a Multivariable Function** **§13.3, Question 49:** Consider the function \( w = w(x, y, z) \). Given by the expression: \[ w = \sqrt{x^2 + y^2 + z^2} \] We are tasked with finding the following partial derivatives: **Part (a):** Find \(\frac{\partial w}{\partial x}\). **Part (b):** Find \(\frac{\partial w}{\partial y}\). **Part (c):** Find \(\frac{\partial w}{\partial z}\). --- *Note: This exercise involves finding the rate of change of the function \( w \) with respect to the variables \( x \), \( y \), and \( z \) individually, while considering the other variables constant. This is a common technique in multivariable calculus called partial differentiation.*
Transcribed Image Text:**Title: Calculating Partial Derivatives of a Multivariable Function** --- **Section 4: Derivatives of a Multivariable Function** **§13.3, Question 49:** Consider the function \( w = w(x, y, z) \). Given by the expression: \[ w = \sqrt{x^2 + y^2 + z^2} \] We are tasked with finding the following partial derivatives: **Part (a):** Find \(\frac{\partial w}{\partial x}\). **Part (b):** Find \(\frac{\partial w}{\partial y}\). **Part (c):** Find \(\frac{\partial w}{\partial z}\). --- *Note: This exercise involves finding the rate of change of the function \( w \) with respect to the variables \( x \), \( y \), and \( z \) individually, while considering the other variables constant. This is a common technique in multivariable calculus called partial differentiation.*
Expert Solution
Step 1: Define problem.

Given function-

w equals w left parenthesis x comma y comma z right parenthesis equals square root of x squared plus y squared plus z squared end root

We have to find the partial derivatives.

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