Differentiator:

With negative feedback applied through a resistor and the input signal through a capacitor, the circuit will perform the mathematical operation of differentiation.  The output voltage then takes up a value proportional to the rate of change of the input voltage - e.g. if the input voltage is the analogue of distance travelled (miles), the output is the analogue of average speed (miles per hour).  The circuit can also be used to produce 'pips' (e.g. calibration markers) when the input signal is a square wave.  (To prevent high frequency instability, it is usual to connect a small capacitor (e.g. 10 μF) across the feedback resistor to reduce gain at frequencies above the required operating frequency).  Figure 10 shows a differentiating circuit.

As in all previous circuits with negative feedback loops, the output voltage takes on a value, which reduces the input difference voltage to zero, and a virtual earth exists on the inverting terminal.  V_in is across C and -v_out across R.