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Clairaut's (Young's) theorem

pagan 5127 Maple
April 21 2008
3

How can Maple arrive at the following, for an unspecified function f(x,y), without knowing sufficient conditions (eg. whether the 2nd partials are continuous)?

> # From the ?diff help-page
> diff(f(x,y),x,y) - diff(f(x,y),y,x);
                                      0

Continuity of integrands isn't generally assumed by int (there's a separate optional parameter which enables it), so why is it assumed for results from diff?
calculus differentiation

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