Question: Chain Rule doesn't work with numerical solutions?

Hi,
     I'm comparing a numerical (asymptotic series solution) to a analytical one in Maple 14, 16 and17 (I have many different machines). I make a substitution S(r) = r^(l+1) R(r) to remove singularities and ask maple to solve for S(r) numerically. Then simply

R(r) = S(r)/ r^(l+1) where S(r) is a numeric procedure
and
diff(R(r), r) = diff(S(r),r)/ r^(l+1) - (l+1) S(r)/ r^(l+2) by the  chain rule, and diff(S(r),r) is another numeric procedure returned by maples dsolve.


Now |
S(r)_numeric agrees with S(r)_analytic,
R(r)_numeric agrees with R(r)_analytic,
diff(S(r),r)_numeric agrees with diff(S(r),r)_analytic
BUT diff(R(r),r)_numeric DOES NTO AGREE WITH  diff(R(r),r)_analytic
 
To me this seems that the formula from the chain rule most be wrong. Does anyone have any ideas? I've attached a .msw file too

Thanks,
Matt
testingDRoutside.mw