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19. If z = f(x,y) has continous partial derivatives, x = s + 2t and y = s - - 2t, show that 2 2 2(0) - ( ;) 2 дz dz ?s at = 2

19. If z = f(x,y) has continous partial derivatives, x = s + 2t and y = s - - 2t, show that 2 2 2(0) - ( ;) 2 дz dz ?s at = 2

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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**Problem 19:** If \( z = f(x, y) \) has continuous partial derivatives, \( x = s + 2t \) and \( y = s - 2t \), show that: \[ \frac{\partial z}{\partial s} \frac{\partial z}{\partial t} = 2 \left( \frac{\partial z}{\partial x} \right)^2 - 2 \left( \frac{\partial z}{\partial y} \right)^2 \]
Transcribed Image Text:**Problem 19:** If \( z = f(x, y) \) has continuous partial derivatives, \( x = s + 2t \) and \( y = s - 2t \), show that: \[ \frac{\partial z}{\partial s} \frac{\partial z}{\partial t} = 2 \left( \frac{\partial z}{\partial x} \right)^2 - 2 \left( \frac{\partial z}{\partial y} \right)^2 \]
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