Covariant derivative

A covariant derivative is like a normal derivative but it's more precise. It helps us figure out how a quantity changes as we move around in a curved space. To understand this more, let's look at a simple example. Imagine you are walking around in a circular room. To figure out how fast the distance between you and the wall is changing, you need to use the covariant derivative. It helps figure out how quickly the distance between you and the wall is changing by taking into account the fact that the room is curved and not flat, so straight line calculations won't work.