This circuit uses an OpAmp with a capacitor between the source and the input. This capacitors current flows through the feedback resistor at the rate: i = C*dv/dt. Because of the derivative term in the capacitors current, the resistor has a voltage drop that is equal to the current times R*C.
Because the only source is AC or DC, the best way to show the differentiator working is by showing the output is the derivative of the input with sinusoids. The green is the input voltage v(t) = sin(wt) and the blue is the output voltage vo(t) = -R*C*w*cos(wt)
