Suppose that z = f(x, y) is differentiable at the point (81, 27) withf;(81, 27) = 6 and f, (81, 27) = -3. If x = t* and y = t° , find dz · when t = 3. dt zp i E='| 1p eTextbook and Media Assistance Used Hint Assistance Used Theorem (Two-Variable Chain Rule) If x = x(1) and y = y(t) are differentiable at t, and if z = f(x, y) is differentiable at the point (x, y) = (x(t), y(t)), then z = f(x(t), y(t)) is differentiable at t and dz dzdx dzdy dt dx dt dy dt where the ordinary derivatives are evaluated at t and the partial derivatives are evaluated at (x, y).
Suppose that z = f(x, y) is differentiable at the point (81, 27) withf;(81, 27) = 6 and f, (81, 27) = -3. If x = t* and y = t° , find dz · when t = 3. dt zp i E='| 1p eTextbook and Media Assistance Used Hint Assistance Used Theorem (Two-Variable Chain Rule) If x = x(1) and y = y(t) are differentiable at t, and if z = f(x, y) is differentiable at the point (x, y) = (x(t), y(t)), then z = f(x(t), y(t)) is differentiable at t and dz dzdx dzdy dt dx dt dy dt where the ordinary derivatives are evaluated at t and the partial derivatives are evaluated at (x, y).
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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