To obtain a differentiation circuit we replace the input resistor of the inverting amplifier with a capacitor as shown in figure 6.9.
Figure 6.9: Differentiation circuit.
Replacing with in the voltage gain gives
Using dV/dt=I/C gives
and thus the same result as above.
The frequency response is shown in figure 6.10.
Figure 6.10: Differentiation circuit frequency response.