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Use the Chain Rule to find the indicated partial derivatives. z = x2 + xy², x = uv + w, y = u + ve" du dv dw when u = 2, v = 2, w = 0 du

Use the Chain Rule to find the indicated partial derivatives. z = x2 + xy², x = uv + w, y = u + ve" du dv dw when u = 2, v = 2, w = 0 du

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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Use the Chain Rule to find the indicated partial derivatives. \[ z = x^2 + xy^2, \quad x = uv^2 + w^3, \quad y = u + ve^w \] Calculate the partial derivatives: \[ \frac{\partial z}{\partial u} = \, \, \, \, \, \, \\ \frac{\partial z}{\partial v} = \, \, \, \, \, \, \\ \frac{\partial z}{\partial w} = \, \, \, \, \, \, \\ \] Given: \[ u = 2, \quad v = 2, \quad w = 0 \] Note: There is an indication where an error is marked with a red "X" next to the calculation for \(\frac{\partial z}{\partial u}\).
Transcribed Image Text:Use the Chain Rule to find the indicated partial derivatives. \[ z = x^2 + xy^2, \quad x = uv^2 + w^3, \quad y = u + ve^w \] Calculate the partial derivatives: \[ \frac{\partial z}{\partial u} = \, \, \, \, \, \, \\ \frac{\partial z}{\partial v} = \, \, \, \, \, \, \\ \frac{\partial z}{\partial w} = \, \, \, \, \, \, \\ \] Given: \[ u = 2, \quad v = 2, \quad w = 0 \] Note: There is an indication where an error is marked with a red "X" next to the calculation for \(\frac{\partial z}{\partial u}\).
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