If you have dv/dt you say to yourself its the derivative of v with respect to t. But in an example of deriving the first kinematic equation for constant acceleration you go from a=dv/dt, to dv=a.dt and then you integrate this equation to give you the velocity. i.e v=u+1/2a(tsquared), using initial conditions. In this sense what is the dv part and what is the dt part? I hope you understand as finding it hard to put into words. Is dv and dt both derivatives?