function finddmdr=dfdx(F,ri,n) 
N=10*n;
rt=logspace(log10(ri(1)),log10(ri(n)),N);
% rt=linspace(ri(1),ri(n),N);
mm=interp1(ri,F,rt,'spline');
        diff1=(mm(1)-mm(2))./(rt(1)-rt(2))+(mm(1)-mm(3))./(rt(1)-rt(3))-...
            (mm(2)-mm(3))./(rt(2)-rt(3));
        diffi=(mm(1:(N-2))-mm(2:(N-1)))./(rt(1:(N-2))-rt(2:(N-1)))....
            -(mm(1:(N-2))-mm(3:N))./(rt(1:(N-2))-rt(3:N))....
            +(mm(2:(N-1))-mm(3:N))./(rt(2:(N-1))-rt(3:N));
        diffn=-(mm(N-1)-mm(N-2))./(rt(N-1)-rt(N-2))+(mm(N-2)-...
            mm(N))./(rt(N-2)-rt(N))+(mm(N-1)-mm(N))./(rt(N-1)-rt(N));
          dmm=[diff1,diffi,diffn];
       
finddmdr=interp1(rt,dmm,ri,'spline');