The differentiator is an inherently marginally stable circuit i.e. it is on the verge of dynamic instability and will often oscillate. Even if it is not actually oscillating the response will have ringing responses to inputs. To understand the operation of this circuit you may, for example, refer to an appropriate book such as ISBN 978-0-521-68780-5, section 5.6 Differentiators. What is needed, as some others above have indicated, is an additional small resistor in series with the usual input capacitor, which acts as a damping control for the second order response function of the circuit. The optimum magnitude of this additional resistor Ri may be calculated from the formula:
Ri = Square root (4 x Rf /omegaT x Ci)
Where Rf is the feedback resistor, omegaT is the transition frequency of the op amp open-loop response (where the response crosses unity gain: note omega is angular frequency) and Ci is the input capacitor. As an example say Rf=10k (10^4), Ci=10n (10^-8), omegaT=10^7 then Ri=630ohm, and allowing for errors in your parameters it will probably be necessary to increase this a bit, depending on the observed signal response.
If you are going to do much electronics it is most desirable you learn something about how to analyze circuits. The reference above will require some effort to understand but it also provides a copy of the PSpice student version which can be of considerable assistance in understanding and designing systems. You may also look at section 5.5 integrators.
Another book of wide interest and practical assistance can be downloaded from:http://www.analog.com/library/analogdialogue/archives/philbrick/computing_amplifiers.html