Taylor series with two variables

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Homework Help Overview

The discussion revolves around the Taylor series expansion for functions of two variables, focusing on the correct formulation of derivatives and their classifications.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are examining the correctness of second-order and third-order derivatives, questioning the terminology used for these derivatives, and discussing the distinction between total and partial derivatives.

Discussion Status

Some participants have provided clarifications regarding the types of derivatives and the notation used, while others are seeking confirmation on the correctness of their expressions and definitions.

Contextual Notes

There appears to be some confusion regarding the notation for derivatives and the inclusion of specific terms in the expressions, which may affect the understanding of the Taylor series expansion.

JasonHathaway
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Hi everyone,

Homework Statement

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The Attempt at a Solution



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It is correct so far.

ehild
 
So the equations of d^2f and d^2f are correct? What are they called? (Total derivatives?)
 
They are second-order and third-order total differentials. And you should write partial derivatives \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y} instead df/dx and df/dy, and so on... And the partial derivative \frac{\partial^2 f}{\partial x\partial y} are not always the same as \frac{\partial^2 f}{\partial y\partial x}.

And you omitted dxdy from the second term of d^2 f

ehild
 
Last edited:

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