Instantaneous velocity is given by the first derivative of distance with respect to time i.e., $v_{\ln }=\frac{d x}{d t}$

Here, the time interval $d t$ is so small that it is assumed that the particle does not change its direction of motion. As a result, both the total path length and magnitude of displacement become equal is this interval of time. Therefore, instantaneous speed is always equal to instantaneous velocity.