Second order active filter design using differentiator
Yes - theoretically, this is possible (on paper). 
However, differentiators are inherently unstable if real operational amplifiers are used (loop gain crosses the 0dB line with a phase margin of app. 0 deg).
It is possible to stabilize differentiators - however, in this case their function is disturbed and their use in filters is heavily limited.
More than that, because differentiators are high pass filters they do not suppress noise components as good as integrators.  That`s the reason, differentiators are not used for filters and oscillators.