> restart;
> G := S*w0^2*b^2*(d^2+0.4*r^2)/(4*L*m*d);

                                 2  2   2       2
                             S w0  b  (d  + .4 r )
                    G := 1/4 ---------------------
                                     L m d

> dS:=diff(G, S);

                                2  2   2       2
                              w0  b  (d  + .4 r )
                    dS := 1/4 -------------------
                                     L m d

> db:=diff(G, b);

                                  2     2       2
                              S w0  b (d  + .4 r )
                    db := 1/2 --------------------
                                     L m d

> dd:=diff(G, d);

                          2  2           2  2   2       2
                      S w0  b        S w0  b  (d  + .4 r )
            dd := 1/2 -------- - 1/4 ---------------------
                        L m                      2
                                            L m d

> dr:=diff(G, r);

                                           2  2
                                       S w0  b  r
                     dr := .2000000000 ----------
                                         L m d

> dw0:=diff(G, w0);

                                    2   2       2
                              S w0 b  (d  + .4 r )
                   dw0 := 1/2 --------------------
                                     L m d

> dm:=diff(G, m);

                                  2  2   2       2
                              S w0  b  (d  + .4 r )
                  dm := - 1/4 ---------------------
                                        2
                                     L m  d

> dL:=diff(G, L);

                                  2  2   2       2
                              S w0  b  (d  + .4 r )
                  dL := - 1/4 ---------------------
                                      2
                                     L  m d

> dS+db+dd+dr+dw+dm+dL;

        2  2   2       2            2     2       2            2  2
      w0  b  (d  + .4 r )   1/2 S w0  b (d  + .4 r )   1/2 S w0  b
  1/4 ------------------- + ------------------------ + ------------
             L m d                   L m d                 L m

                   2  2   2       2                    2  2
               S w0  b  (d  + .4 r )   .2000000000 S w0  b  r
         - 1/4 --------------------- + ---------------------- + dw
                           2                   L m d
                      L m d

                   2  2   2       2            2  2   2       2
               S w0  b  (d  + .4 r )       S w0  b  (d  + .4 r )
         - 1/4 --------------------- - 1/4 ---------------------
                         2                         2
                      L m  d                      L  m d

> dG := sqrt(%);

                   2  2   2       2            2     2       2
                 w0  b  (d  + .4 r )   1/2 S w0  b (d  + .4 r )
  dG := sqrt(1/4 ------------------- + ------------------------
                        L m d                   L m d

                   2  2           2  2   2       2
           1/2 S w0  b        S w0  b  (d  + .4 r )
         + ------------ - 1/4 ---------------------
               L m                        2
                                     L m d

                           2  2                  2  2   2       2
           .2000000000 S w0  b  r            S w0  b  (d  + .4 r )
         + ---------------------- + dw - 1/4 ---------------------
                   L m d                               2
                                                    L m  d

                   2  2   2       2
               S w0  b  (d  + .4 r )
         - 1/4 ---------------------)
                       2
                      L  m d

>