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dz Use the Chain Rule to find when = a? + xy + y², z = nd = 2s – t, y = st. || |

dz Use the Chain Rule to find when = a? + xy + y², z = nd = 2s – t, y = st. || |

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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**Using the Chain Rule to Find \(\frac{\partial z}{\partial t}\):** Given: \[ z = x^2 + xy + y^2, \] and \[ x = 2s - t, \quad y = st. \] Determine \(\frac{\partial z}{\partial t}\) from the following options: 1. \(\frac{\partial z}{\partial t} = 4x - y + xt + 2yt\) 2. \(\frac{\partial z}{\partial t} = -2x - y + xt + 2yt\) 3. \(\frac{\partial z}{\partial t} = -2x - y + xs + 2ys\) 4. \(\frac{\partial z}{\partial t} = 4x + 2y + xs + 2ys\) 5. \(\frac{\partial z}{\partial t} = 4x + 2y + xt + 2yt\) 6. \(\frac{\partial z}{\partial t} = -2x + 2y + xs + 2ys\) Use these equations to apply the chain rule and find the correct expression for \(\frac{\partial z}{\partial t}\).
Transcribed Image Text:**Using the Chain Rule to Find \(\frac{\partial z}{\partial t}\):** Given: \[ z = x^2 + xy + y^2, \] and \[ x = 2s - t, \quad y = st. \] Determine \(\frac{\partial z}{\partial t}\) from the following options: 1. \(\frac{\partial z}{\partial t} = 4x - y + xt + 2yt\) 2. \(\frac{\partial z}{\partial t} = -2x - y + xt + 2yt\) 3. \(\frac{\partial z}{\partial t} = -2x - y + xs + 2ys\) 4. \(\frac{\partial z}{\partial t} = 4x + 2y + xs + 2ys\) 5. \(\frac{\partial z}{\partial t} = 4x + 2y + xt + 2yt\) 6. \(\frac{\partial z}{\partial t} = -2x + 2y + xs + 2ys\) Use these equations to apply the chain rule and find the correct expression for \(\frac{\partial z}{\partial t}\).
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