Invertibility of an ideal differentiator Is the system $y(t)= dx(t)/dt$  invertible or not?
If yes, please determine the inverse system for it.
It is not. It suffices to find a counter example. Let me tell you that "I am flat". Could you derive my actual value?

So, any constant function $f(t) =c$ is differentiable, and have the same derivative, $f'(t)=0$. Only from knowing that  $f'(t)=0$, you cannot recover the original (constant) function. Hence the system is not invertible.