Taylor series with two variables

[JasonHathaway]

Hi everyone,

Homework Statement

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Homework Equations

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The Attempt at a Solution

 

[ehild]

It is correct so far.

ehild

 

[JasonHathaway]

So the equations of d^2f and d^2f are correct? What are they called? (Total derivatives?)

 

[ehild]

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