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dV/dx = dV/dy = dV/dz ?

(these should be partial derivatives)

I am trying to show L = r x [nab] commutes with any radial function V(r) meaning that for any function f

r x [nab] ( V(r) * f) - V(r) * r x [nab] f = 0

most of the terms cancel out but I am left with

(y dV/dz - x dV/dz -zdV/dy + xdV/dy + z dVdx - y dV/dx) * f

or (y (dV/dz - dV/dx) + x( dV/dy - dVdz ) +z( dV/dx - dV/dy ) ) * f

If the partial derivatives cancel then I am done. If not I have no clue how to continue but I do know the final answer must be zero.