What's the difference between these differential operators?

[corona7w]

I'm learning fluid mechanics, and I am confused about the following differential operators. What's the difference between each?

 

[Thaakisfox]

the first one is the so called convective derivative. This arises from the fact that in the euler picture we have a velocity field, that is a first order tensor field or vector field, describing the velocity as a function of space and time. Hence velocity or any other vector field doesn't change only by time but by place too. So the differential operator is.

The second one is the variational derivative.

The third one is the usual partial derivative.