How the following relation can be proved: If $$l\left(x\right)=\left(x-x_{0}\right)\left(x-x_{1}\right)...\left(x-x_{k}\right)$$ if a polynomial,then
$$l_{j}\left(x\right)=\frac{l\left(x\right)}{l^{'}\left(x_{j}\right)\left(x-x_{j}\right)}$$ where $$l_{j}\left(x\right)=\prod_{m=0}^{k}\frac{x-x_{m}}{x_{j}-x_{m}}$$ when $m$ and $j$ are not equal. I tried to see thr formula in some example, but still I'm not able to proof that.