How to calculate $f(n)=1\binom{n}{1}+2\binom{n}{2}+3\binom{n}{3}.....n\binom{n}{n}$ $$f(n)=1\binom{n}{1}+2\binom{n}{2}+3\binom{n}{3}.....n\binom{n}{n}$$

Is there a formula for this?
$f(x) = (1 + x)^n$, $S = f'(1) = n\cdot 2^{n-1}$
Hint: Expand $n(1+x)^{n-1}$ using the binomial theorem, then put $x=1$.