**Question**: If $(1+x)^n=\binom{n}{0}+\binom{n}{1}x+\binom{n}{2}x^2+\dotsm+\binom{n}{n}x^n$, prove that $\binom{n}{1}-2\binom{n}{2}+3\binom{n}{3}-\dotsm+(-1)^{n-1}n\binom{n}{n}=0$

**My attempt**: I wrote the expression for $\binom{n}{k}$ for each term in the L.H.S and then tried to simplify but could not reach the R.H.S.

Please help. I have no idea on how to begin. I am not allowed to use calculus.