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7. Let w = 8x? + 6 y² +2z° ;x = r²; y =t*; z =r² Find A) -321 + 481- + 201º В) -321 +481' + 201° - = -321 +481° + 2017 D) - -321° +481' + 20rs E) -32122

7. Let w = 8x? + 6 y² +2z° ;x = r²; y =t*; z =r² Find A) -321 + 481- + 201º В) -321 +481' + 201° - = -321 +481° + 2017 D) - -321° +481' + 20rs E) -32122

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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The problem presented is to find the partial derivative \(\frac{\partial w}{\partial t}\) for the function \(w = 8x^2 + 6y^2 + 2z^5\) given the parameterizations \(x = t^{-2}\), \(y = t^4\), and \(z = t^2\). Options: - A) \(\frac{\partial w}{\partial t} = -32t^7 + 48t^{-5} + 20t^9\) - B) \(\frac{\partial w}{\partial t} = -32t^{-5} + 48t^7 + 20t^9\) - C) \(\frac{\partial w}{\partial t} = -32t^{-5} + 48t^9 + 20t^7\) - D) \(\frac{\partial w}{\partial t} = -32t^9 + 48t^7 + 20t^{-5}\) - E) \(\frac{\partial w}{\partial t} = -32t^{22}\) The task is to select the correct expression for \(\frac{\partial w}{\partial t}\) by differentiating \(w\) using the provided expressions for \(x\), \(y\), and \(z\).
Transcribed Image Text:The problem presented is to find the partial derivative \(\frac{\partial w}{\partial t}\) for the function \(w = 8x^2 + 6y^2 + 2z^5\) given the parameterizations \(x = t^{-2}\), \(y = t^4\), and \(z = t^2\). Options: - A) \(\frac{\partial w}{\partial t} = -32t^7 + 48t^{-5} + 20t^9\) - B) \(\frac{\partial w}{\partial t} = -32t^{-5} + 48t^7 + 20t^9\) - C) \(\frac{\partial w}{\partial t} = -32t^{-5} + 48t^9 + 20t^7\) - D) \(\frac{\partial w}{\partial t} = -32t^9 + 48t^7 + 20t^{-5}\) - E) \(\frac{\partial w}{\partial t} = -32t^{22}\) The task is to select the correct expression for \(\frac{\partial w}{\partial t}\) by differentiating \(w\) using the provided expressions for \(x\), \(y\), and \(z\).
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