The differentials of a spectral sequence

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Suppose we are on the $E_r$ page and the lattice either consists of 0 or $\mathbb{Q}[x,y]$ in each entry. Suppose in particular that the points $(p,q)$ and $(r, s)$ (and "their codomains") are equal to $\mathbb{Q}[x,y]$. If I know that the differential $d_r^{p,q}$ takes $x$ to an element $z$. Can I conclude that the differential $d_r^{r,s}$ also takes $x$ to $z$?