What is the physical meaning of the derivative

4. Physical meaning of the derivative

The current speed of the uniform movement.
It is assumed that the function \ (x (t) \) describes the dependence of the coordinate of a point mass on time. The average speed in the time interval is the ratio of the movement to the time required:
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In order to calculate the current speed, one determines the limit value of the ratio when tending towards zero. If this limit exists, it matches :.
A steadily accelerated straight line movement.
One assumes that a point mass moves on a straight line and that the function \ (v (t) \) gives its velocity at time \ (t \). The average acceleration in the time interval is the ratio of the changed speed to the changed time. In order to calculate the acceleration at the point in time \ (t \), we allow it to tend towards zero. It is .
It is assumed that the function \ (q (t) \) represents the ratio of the charge that passes through a line of a given cross-section to the time. In order to calculate the magnitude of the current \ (I \) at a given point in time, the average magnitude of the current can be represented as the ratio.
The instantaneous magnitude of the current is then the limit value of the ratio when the change in time tends towards zero, i.e. the derivative of the function \ (q (t) \):