Prove the identity about interpolation

Question

I am studying numerical analysis and I have difficulty with the following exercise concerning interpolation: $$\sum_{i=0}^n \dfrac{x_i^n}{\prod_{j=0,j≠i}^n(x_i-x_j)}=1，$$where $x_i$ are pairwisely unequal.I want to use Lagrange interpolation to prove it, but failed, can anyone help me?

Answer 1

Hint. Try to match $\frac{d^n}{dx^n} \ell_i(x)$ with the product from the problem.