Find the value of at the point (1,1,1) if the equation 3xy +z°x-2yz = 2 defines z as a function of the two independent variables x and y and the partial derivative exists. ..... dz ax (1,1,1)
Find the value of at the point (1,1,1) if the equation 3xy +z°x-2yz = 2 defines z as a function of the two independent variables x and y and the partial derivative exists. ..... dz ax (1,1,1)
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 Statement:**
Find the value of \(\frac{{\partial z}}{{\partial x}}\) at the point (1,1,1) if the equation \(3xy + z^3x - 2yz = 2\) defines \(z\) as a function of the two independent variables \(x\) and \(y\) and the partial derivative exists.
**Solution Requirement:**
\[
\left. \frac{{\partial z}}{{\partial x}} \right|_{(1,1,1)} = \boxed{\quad}
\]
- The task is to compute the partial derivative of \(z\) with respect to \(x\) at the specified point.
- The derivative should be evaluated considering the relation \(3xy + z^3x - 2yz = 2\) where \(z\) is dependent on \(x\) and \(y\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1031dce-282c-4eb1-aa3d-5d70b67299d5%2F3fe3749c-1da9-4878-a4e4-59054eb6a902%2Ff2ij2ws_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the value of \(\frac{{\partial z}}{{\partial x}}\) at the point (1,1,1) if the equation \(3xy + z^3x - 2yz = 2\) defines \(z\) as a function of the two independent variables \(x\) and \(y\) and the partial derivative exists.
**Solution Requirement:**
\[
\left. \frac{{\partial z}}{{\partial x}} \right|_{(1,1,1)} = \boxed{\quad}
\]
- The task is to compute the partial derivative of \(z\) with respect to \(x\) at the specified point.
- The derivative should be evaluated considering the relation \(3xy + z^3x - 2yz = 2\) where \(z\) is dependent on \(x\) and \(y\).
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