Try googling
spherical polar coordinates jacobian
or even
derivation spherical polar coordinates jacobian
One hit that might be useful is here
cheers, i got upto here.
d(x,y,z) = I sinAcosB rsinAcosB -rsinAsinB I
d(r,A,B) I sinAsinB rcosAsinB rsinAcosB I
I cosA -rsinA 0 I
= [(sinAcosB)(rcosAsinB)] - [(sinAsinB)(rcosAcosB)]
but i dont know what to do next in order to show that
d(x,y,z) = r^2sinA
d(r,A,B)