What about slew rate?

An answer:

pict

\begin{array}{rcl} v_{OUT} = a_{V} \cdot A_{sig} \cdot \sin (ωt) \\ \frac{\partial v_{OUT}}{∂t} = ω \cdot a_{V} \cdot A_{sig} \cdot \cos (ωt) \\ max (\frac{\partial v_{OUT}}{∂t}) = ω \cdot a_{V} \cdot A_{sig} \cdot \cos (0) = ω \cdot a_{V} \cdot A_{sig} = 2 πf \cdot a_{V} \cdot A_{sig} \end{array}

Hence the slew rate must be at least $SR = 50 πf$ [V/s].