Find the second partial derivative of the function f(z, y, z) = 2°yz+ at the point (1, 1, 1). yz

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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sin z,
sin z,
etc.
Question 14.1 Section 14.1 Progress Check Question 1
of the function f(e, y, 2) = z'yz+
dydz
at the point (1, 1,1).
yz
Find the second partial derivative
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The Mixed Partials Are Equal
In all these examples note that the pairs of mixed partial derivatives, such as &²f/0z Oy and d²f/@yOr,
or 8 f/8z0z and 02f/Dx 0z, are equal. It is a basic and perhaps surprising fact that this is always the
case for C functions. We shall prove this in the next theorem for functions f(r, y) of two variables, but
the proof can be readily extended to functions of n variables.
Theorem 1 Equality of Mixed Partials
If f(r.v) is of class CP (is twice continuously differentiable), then the mixed partial derivatives are equal;
Transcribed Image Text:sin z, sin z, etc. Question 14.1 Section 14.1 Progress Check Question 1 of the function f(e, y, 2) = z'yz+ dydz at the point (1, 1,1). yz Find the second partial derivative Feedback Try again Submit .... The Mixed Partials Are Equal In all these examples note that the pairs of mixed partial derivatives, such as &²f/0z Oy and d²f/@yOr, or 8 f/8z0z and 02f/Dx 0z, are equal. It is a basic and perhaps surprising fact that this is always the case for C functions. We shall prove this in the next theorem for functions f(r, y) of two variables, but the proof can be readily extended to functions of n variables. Theorem 1 Equality of Mixed Partials If f(r.v) is of class CP (is twice continuously differentiable), then the mixed partial derivatives are equal;
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