Simple Differentiator with OpAmp - response function
I see three main errors :-

First, your transfer function is missing a term in \$\omega_P\$ in the numerator.

\$A(s) = \dfrac{-A_0\omega_Ps}{s^2+s(\omega_P+\frac{1}{RC})+\frac{\omega_P(A_0+1)}{RC}}\$

Second, the natural frequency should be :-

\$\omega_{PV} = \sqrt\frac{\omega_P(A_0+1)}{RC}\$

Third, your bode plot should fall at 20dB/decade above the natural frequency.

In practice, real differentiators made this way tend to have high Q (low damping) giving a high peak in the transfer function at the natural frequency causing severe ringing. This can be reduced by putting a small resistor in series with the capacitor.