dpp3daf12a = (p2f1*(((1 - (1 - a12)*(1 - af12)*(1 - e5))*
         (a12*(-1 + u1b3r12 + u2b3r12 - u3b12r3) + 2*u3b12r3))/2 + 
       ((1 - a12)*(1 - e5)*(-(a12*(-2 + af12)*(-1 + u1b3r12 + u2b3r12)) + 
          (-2 + a12)*af12*u3b12r3))/2))/(1 - (1 - a12)*(1 - af12)*(1 - e5))^2
 
p2f1e = (a2f1*(2 + n1 + n3 + 2*n1*n3))/(6*(1 - (1 - e4)*n1*n2*n3))
 
dpp3daf12b = (a2f1*(2 + n1 + n3 + 2*n1*n3)*
      (((1 - (1 - a12)*(1 - af12)*(1 - e5))*
         (a12*(-1 + u1b3r12 + u2b3r12 - u3b12r3) + 2*u3b12r3))/2 + 
       ((1 - a12)*(1 - e5)*(-(a12*(-2 + af12)*(-1 + u1b3r12 + u2b3r12)) + 
          (-2 + a12)*af12*u3b12r3))/2))/
     (6*(1 - (1 - a12)*(1 - af12)*(1 - e5))^2*(1 - (1 - e4)*n1*n2*n3))
 
nsubs = {n1 -> 1 - a1f2 - a1f3, n2 -> 1 - a2f1 - a2f3, n3 -> 1 - a3f1 - a3f2}
 
dpp3daf12c = (a2f1*(4 - a1f2 - a1f3 - a3f1 + 2*(1 - a1f2 - a1f3)*
        (1 - a3f1 - a3f2) - a3f2)*(((1 - (1 - a12)*(1 - af12)*(1 - e5))*
         (a12*(-1 + u1b3r12 + u2b3r12 - u3b12r3) + 2*u3b12r3))/2 + 
       ((1 - a12)*(1 - e5)*(-(a12*(-2 + af12)*(-1 + u1b3r12 + u2b3r12)) + 
          (-2 + a12)*af12*u3b12r3))/2))/
     (6*(1 - (1 - a1f2 - a1f3)*(1 - a2f1 - a2f3)*(1 - a3f1 - a3f2)*(1 - e4))*
      (1 - (1 - a12)*(1 - af12)*(1 - e5))^2)