but

u can take the case of a body moving uniform circular motion

then dIvI /dt = 0

because IvI  means the speed which doesnot change with time

but dv/dt means the change of velocity

which  wont be zero  bcos it changes with time

so dv/dt  0

that is I dv/dt I  0

they are same things.

 imagine the velocity time graph is like a mountain. ( i mean linear increasing, then peak, then linear decreasing)

the 2 expressions will gave the same result.

note that the calculus operator as far as my knowledge expends is only an operator and does not have any algebraic meaning.

there is no maening to x + d/dt + d/dx + y = 0

so mod function will mean nothing.