{Derivative[0, 2][\[Omega]0][s, m2] -> 
  (-4*\[Omega]0[s, m2])/(m2*(16*m2 + s)) - 
   ((32*m2 + s)*Derivative[0, 1][\[Omega]0][s, m2])/(16*m2^2 + m2*s), 
 Derivative[1, 0][\[Omega]0][s, m2] -> -(\[Omega]0[s, m2]/s) - 
   (m2*Derivative[0, 1][\[Omega]0][s, m2])/s, 
 Derivative[1, 1][\[Omega]0][s, m2] -> (4*\[Omega]0[s, m2])/(16*m2*s + s^2) - 
   Derivative[0, 1][\[Omega]0][s, m2]/(16*m2 + s), 
 Derivative[1, 0, 0][G][s, t, m2] -> 
  (m2*(16*m2*s - t*(3*s + 2*t))*\[Omega]0[s, m2]*r[9][s, t, m2])/
    ((s + t)*(-4*m2*s + t*(s + t))^2) - 
   (m2*(16*m2 + s)*r[9][s, t, m2]*Derivative[0, 1][\[Omega]0][s, m2])/
    (2*(s + t)*(-4*m2*s + t*(s + t))), Derivative[0, 1, 0][G][s, t, m2] -> 
  -((m2*s^2*(16*m2 + s)*\[Omega]0[s, m2]*r[9][s, t, m2])/
     (t*(s + t)*(-4*m2*s + t*(s + t))^2)) + 
   (m2*s*(16*m2 + s)*r[9][s, t, m2]*Derivative[0, 1][\[Omega]0][s, m2])/
    (2*t*(s + t)*(-4*m2*s + t*(s + t))), Derivative[0, 0, 1][G][s, t, m2] -> 
  (s*(s + 2*t)*\[Omega]0[s, m2]*r[9][s, t, m2])/(-4*m2*s + t*(s + t))^2}