Bandwidth of the Derivative of a Message
Hint:

Checking a table of Fourier transform properties you'll find that the Fourier transform of the derivative is given by

$$\mathcal{F}\left\{\frac{dm(t)}{dt}\right\}=j\omega M(\omega)\tag{1}$$

where $M(\omega)$ is the Fourier transform of $m(t)$. Now if $M(\omega)$ is band-limited, what does this tell you about the Fourier transform of $dm(t)/dt$?