In a differentiator circuit using an operational amplifier, how does the gain relate to the differential input voltage?

The output of a differential amplifier is the product of its closed‑loop gain and the difference between the two input voltages, so the output voltage is simply the differential input voltage multiplied by the gain. In other words, \(V_{\text{out}} = A_d \,(V_+ - V_-)\). Thus, if the gain is 5 and the two inputs differ by 2 mV, the output will be 10 mV. The amplifier will saturate if the product exceeds its supply limits, so the usable differential range is limited by the supply rails. This linear relationship lets you calculate the output directly from the differential input and the chosen gain.