Differential operator question

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# Differential operator question

Submitted by Thomas2054 on Mon, 07/29/2013 - 12:46

Forums:

In working through a problem on the application of Christoffel symbols^{}, I came across an author’s answer to a problem

_αα^i = ∂∂x^α( ∂¯x^r∂x ) ∂x^i∂¯x^r = ( d_α ∂¯x^r∂x )∂x^i∂¯x^r = d_α δ_α^i

which confused me, since I have not see the a ”d” operator used before

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## Versions

(v1) by Thomas2054 2013-07-29

## Differential operator question

I cannot ask this question without figuring out how to enter the LaTeX string. It is not displaying correctly in the original, which was posted before I was done.

The LaTeX equation appeared correclty when constructed at http://www.codecogs.com/latex/eqneditor.php. What am I doing wrong to have it appear correclty here?

My question is this. How does the author appear to take the last partial derivative into the parenthesis and effectively cancel the x, bar r terms and end up with the Kronecker delta result?

Thanks.

## Differential operator question

Here is an image of the equation I am trying to enter.

## Differential operator question

Not having much luck with this site.

I used to post an image, and that did not work, either.

My image is at http://planetmath.org/node/87495

Among other things, the fact that Ctrl-V does not paste things is annoying.

Is this site really this hard to use?

## Re: Differential operator question (how to include graphics)

`\includegraphics{Eq1.jpg}`

Works for me.

These mechanisms will be streamlined eventually. Sorry for any frustration in the mean times.

## Also, to post LaTeX you need to put the expression in $'s

$\Gamma_{{\alpha\alpha}}^{{i}}=\frac{\partial}{\partial x^{{\alpha}}}\left(% \frac{\partial\bar{x}^{{r}}}{\partial x}\right)\frac{\partial x^{{i}}}{% \partial\bar{x}^{{r}}}=\left(d_{{\alpha}}\,\frac{\partial\bar{x}^{{r}}}{% \partial x}\right)\frac{\partial x^{{i}}}{\partial\bar{x}^{{r}}}=d_{{\alpha}}% \,\delta_{{\alpha}}^{{i}}$