Natural Science Forum / Physics / General Physics / July 2008

From Osher Doctorow

Maybe it was "too elementary" :>)   The correct equations are:

1) Dxy(exp(xy)) = (1 + xy)exp(xy)
2) Dxy(log(xy)) = 0
3) Dxy(exp(kxy)) = k(1 + xy)exp(kxy)

To prove (1), we proceed as follows:

4) Dy(Dx(exp(xy)) = Dy(yexp(xy)) = exp(xy) + yDy(exp(xy)) = exp(xy) +
yx(exp(xy)).

To prove (2), we proceed as follows:

5) Dxy(log(xy)) = Dy(Dx(log(xy))) = Dy(1/x) = 0

The proof of (3) is like that of (4).

Osher Doctorow