If a multivariate function has continuous partial derivatives, the order in which the derivatives are calculated does not matter. Thus, for example, the function f(x, y) of two variables has equal third partials 8³ da ² dy f(x, y) = 2³ əyəx² f (x, y). (a) How many fourth partial derivatives does a function of three variables have? (b) Prove that a function of n variables has ("+-¹) rth partial derivatives.
If a multivariate function has continuous partial derivatives, the order in which the derivatives are calculated does not matter. Thus, for example, the function f(x, y) of two variables has equal third partials 8³ da ² dy f(x, y) = 2³ əyəx² f (x, y). (a) How many fourth partial derivatives does a function of three variables have? (b) Prove that a function of n variables has ("+-¹) rth partial derivatives.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Problem 1P
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![If a multivariate function has continuous partial derivatives, the order in which the
derivatives are calculated does not matter. Thus, for example, the function f(x, y) of
two variables has equal third partials
8³
da ² dy f(x, y) =
2³
əyəx² f (x, y).
(a) How many fourth partial derivatives does a function of three variables have?
(b) Prove that a function of n variables has ("+-¹) rth partial derivatives.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbf0f61f3-0026-4166-9371-72c554f7c10e%2Fed843d95-eba1-4a97-9ad1-c5b2b8c51505%2Ffgrf6mx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:If a multivariate function has continuous partial derivatives, the order in which the
derivatives are calculated does not matter. Thus, for example, the function f(x, y) of
two variables has equal third partials
8³
da ² dy f(x, y) =
2³
əyəx² f (x, y).
(a) How many fourth partial derivatives does a function of three variables have?
(b) Prove that a function of n variables has ("+-¹) rth partial derivatives.
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