Discrete Time Fourier Transform of the signal represented by $x[n] = n^2 a^n u[n]$ I have a homework problem that I am just not sure where to start with.  I have to take the Discrete Time Fourier Transform of a signal represented by:
$$x[n] = n^2 a^n u[n]$$
given that $|a| < 1$,  $\Omega_0 < \pi$, and u[n] being the unit step function.
There is a hint saying that "Calculus and derivatives will help!" but that actually confuses me more than it helps.  However, regardless, I'm just not sure how to even get started evaluating that.  I know how to take the DTFT of a signal, but just can't figure out how to get it into a usable form.  I also am allowed to use the following conversion:
$$ x[n] = a^nu[n] \iff X(\Omega) = \frac{e^{j\Omega}}{e^{j\Omega} - a}$$
I am not looking for the answer, but rather just some pointers as to how to start manipulating the original signal.

To include this as the answer that most helped me, since it was just as a comment to my original post.  The most straightforward solution seemed to be by using the property of the Discrete Time Fourier Transform for when you are multiplying by n in the time domain, that corresponds to a derivation in the Fourier/frequency domain.
Therefore, the solution would just be to take the Fourier transform from the provided conversion, and then taking the second derivative of that.  This is the solution that I got after doing so:
$$X(\Omega) = \frac{a^3e^{j\Omega} - ae^{j3\Omega}}{(e^{j\Omega} - a)^4}$$
