Hello all,

I was wondering if there was a resource on different groupings of derivatives.

for instance:

$\displaystyle U_{{i}}{\frac {d}{dx}}U_{{i}} ={\frac {1}{2}} {\frac {d}{dx}}U_{{i}}^2
$

what happens if:
$\displaystyle U_{{i}}{\frac {d}{dx}}U_{{j}} = ???
$

I am working on an equation and seem to be running into situations like this!

Thank you!