We will first assume that the op amp used here is an ideal op amp. We know that the voltage at both inverting and non inverting terminals of an ideal op amp is same. As the electric potential at non inverting terminal is zero since it is grounded. The electric potential of inverting terminal is also zero, as the opamp is ideal. Because, we know that the electric potential at non – inverting and inverting terminals. It is also known to us that the current entering through inverting and non inverting terminal of an ideal op amp is zero.
Considering, these conditions of an ideal op amp, if we apply Kirchhoff Current Law at node 1 of the op amp differentiator circuit, we get,
The above equation shows that the output voltage is the derivative of the input voltage.