Prove that the Weiertrass function is biperiodic

Question

I am reading the chapter on elliptic functions in complex analysis by ahlfors, who used the following formula in his argument that the Weiertrass function is biperiodic
We let $$\wp＝\frac{1}{z^2}+\sum_{\omega\neq 0} \left(\frac{1}{(z-\omega)^2}-\frac{1}{\omega^2}\right)$$ He said it's a little bit more difficult to verify directly, so we take the derivative $$\dot{\wp}＝-2\sum_{\omega}\frac{1}{(z-\omega)^3}$$ And then he says that the last one is obviously biperiodic, and I want to know how that works, and how does it work out that the function is biperiodic just because the derivative is biperiodic