$($Difficulty: $x***$ Consider a signal $x[n]$ and its DTFT $x(e^j).$ Assume $x(e^j)$ is differentiable. Compute the inverse DTFT of $j\frac{d}{d}x(e^j).$

$($Difficulty: $***)$ Consider the length$-L$ signal

$x[n]=\{\begin{array}{cc}1,& 0nM-1\\ 0,& MnL-1\end{array}$

Write out the closed$-$form analytical expression for its DFT coefficients $x[k].$