Inverse discrete time Fourier transform with differentiation
Hint:
differentiate from Fourier Transform equation:
$$X(e^{j\omega})= \sum\limits_{n=- \infty }^{\infty}x[n]e^{-jn\omega} \Rightarrow \frac{d}{d\omega}X(e^{j\omega})= \frac{d}{d\omega}\sum\limits_{n=- \infty }^{\infty}x[n]e^{-jn\omega}$$
and then find what you want.