Let $f$ be an entire function of order $ρ<∞$. Assume that $f$ does not vanish identically on $ℂ$. Then, we know that $f$ has a Hadamard's product formula

$f(s)=exp(g(s))s^{r}∏_{k=1}^{∞}(((s_{k}-s)/(s_{k})))exp( (s/(s_{k})))$

the integer $r$ is the order of vanishing of $f$ at $s=0$, the $s_{k}$ are the other zeros of $f$ listed with multiplicity, $g$ is a polynomial of degree at most $ρ$, and the product converges uniformly in bounded subsets of $ℂ$.
My question is how I can deduce directely a Hadamard's product formula for the derivative $f′$ from the one of the function $f$.