Compute the first-order partial derivatives of the function. 2х W = (x² + y² + z?)"2 (Use symbolic notation and fractions where needed.) -18:2(? + y² + 2) -x(? +y? + ?)* dw dx Incorrect dw ду -18x) +. dw dz +z II
Compute the first-order partial derivatives of the function. 2х W = (x² + y² + z?)"2 (Use symbolic notation and fractions where needed.) -18:2(? + y² + 2) -x(? +y? + ?)* dw dx Incorrect dw ду -18x) +. dw dz +z II
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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![**Compute the first-order partial derivatives of the function.**
\[ w = \frac{2x}{(x^2 + y^2 + z^2)^{\frac{9}{2}}} \]
(Use symbolic notation and fractions where needed.)
---
**Partial Derivative with respect to \(x\):**
\[\frac{\partial w}{\partial x} = \frac{-18x^2(x^2 + y^2 + z^2)^{\frac{7}{2}} - x(x^2 + y^2 + z^2)^{\frac{9}{2}}}{(x^2 + y^2 + z^2)^9}\]
(Incorrect)
---
**Partial Derivative with respect to \(y\):**
\[\frac{\partial w}{\partial y} = -18xy(x^2 + y^2 + z^2)^{-\frac{11}{2}}\]
---
**Partial Derivative with respect to \(z\):**
\[\frac{\partial w}{\partial z} = -18xz(x^2 + y^2 + z^2)^{-\frac{11}{2}}\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b297299-7dbb-4df0-a4de-f3e6aa8c53a3%2Fbbfe9d93-914e-4ba7-a914-b983f1bde366%2F52e4hli_processed.png&w=3840&q=75)
Transcribed Image Text:**Compute the first-order partial derivatives of the function.**
\[ w = \frac{2x}{(x^2 + y^2 + z^2)^{\frac{9}{2}}} \]
(Use symbolic notation and fractions where needed.)
---
**Partial Derivative with respect to \(x\):**
\[\frac{\partial w}{\partial x} = \frac{-18x^2(x^2 + y^2 + z^2)^{\frac{7}{2}} - x(x^2 + y^2 + z^2)^{\frac{9}{2}}}{(x^2 + y^2 + z^2)^9}\]
(Incorrect)
---
**Partial Derivative with respect to \(y\):**
\[\frac{\partial w}{\partial y} = -18xy(x^2 + y^2 + z^2)^{-\frac{11}{2}}\]
---
**Partial Derivative with respect to \(z\):**
\[\frac{\partial w}{\partial z} = -18xz(x^2 + y^2 + z^2)^{-\frac{11}{2}}\]
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