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On Dec 30, 5:08 pm, "Thomchad" <chadef...@xxxxxxxxx> wrote:
> Hi all,
>
> Take a function f(x,y,z,...)
>
> On the diagonal of the Hessian matrix, I understand we have a
> "standard" partial derivative. We write (using latex): \frac{\partial^2
> f}{\partial x^2}.
>
> Now, off diagonal, we write: \frac{partial^2 f}{\partial x \partial y}.
>
> There are two things I do not understand:
> 1. how to manipulate the "partial" signs. Are they "multiplied", which
> explains the ^2? I thought the partial sign was just some convention to
> say "partial"
> 2. What does it mean to have \partial x \partial y in the denominator?
> Could someone please give me an example? Do I take the partial with
> respect to x? to y? to both?
>
> Hopefully I make some sense. Thank you for your help, which will be
> greatly appreciated.
> Tom
The exponent 2 in the numerator refers to the second partial
derivative, i.e. the partial derivative of the partial derivative. The
expression in the denominator tells you which partial derivative is
taken first and which is second.
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