Find the value of $\sum_{k=1}^{n} k \binom {n} {k}$ I was assigned the following problem: find the value of $$\sum_{k=1}^{n} k \binom {n} {k}$$ by using the derivative of $(1+x)^n$, but I'm basically clueless. Can anyone give me a hint?

Recall that 
$$
(1+x)^n =  \sum_{k=0}^{n} x^k \binom {n} {k}
$$
and thus 
$$
((1+x)^n)' =  \sum_{k=1}^{n} k x^{k-1} \binom {n} {k}
$$
Now, calculate the left-hand side, and then think which value of $x$ could be a good choice.
