Manipulation of a matrix full of differentials

Hi All.

I'm a bit new to Maxima, so if my question has an obvious answer, please
point me to the correct manual :)

My question is the following.  Say I have a matrix full of
differentials, defining, eg. the Jacobian of a coordinate transform:

J:matrix(['diff(x,u), 'diff(y,u), 'diff(z,u)], ['diff(x,v), 'diff(y,v),
'diff(z,v)],['diff(x,v), 'diff(y,v), 'diff(z,v)]);

And now I want to get the analytical inverse of this matrix. However,
determinant(J) gives me zero, as if it is actually evaluating the
differentials, while determinant('J) does not quite do the trick either.

Any hints appreciated.

Thanks
Neilen
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