The differentiation property of the continuous Fourier transform of a signal $x(t)$ (aperiodic, with a finite energy, and that respects Dirichlet's criterion) say that ($x(t)$ and $X(f)$ are known):
$$x(t)\iff X(f)$$
$$y(t)=\frac{dx(t)}{dt}\iff Y(f)=j2\pi fX(f)$$
How do I know that $y(t)$ is aperiodic, with a finite energy? This is necessary to define $Y(f)$!
Thank you.
As $x(t)$ is known, you can calculate the signal energy through: $$E_{\infty}=\lim\limits_{T \to \infty}\int_{-T}^{T}|x(t)|^{2}dt$$
Which can also be done for $y(t)$
Regarding aperiodicity, you just need to show that:
$$\forall t,\,\,\, \nexists \,\,\, T_{0} \,\,|\,\, y(t)=y(t+T_{0})$$