I am following Hatcher's notes on spectral sequences. On page 522 an exact couple $(A, E, i, j, k)$ is defined. You can construct a derived exact couple easily from this to get your desired $E'$ however constructing the new differential from this information is said to be not so easy in practice. I would like to know why this is, to me it seems that $d'$ is simply $j'k'$. Is this a difficult thing to calculate or is it simply tedious? It seems to be the same opinion everywhere that given a term in a spectral sequence $(E^r, d_r)$, calculating $E^{r+1}$ is easy and $d_{r+1}$ just isn't practically possible with the given information.

I'd like to think there is some algorithm where you give a pair $(E^r, d_r)$ and it spits out a pair $(E^{r+1},d_{r+1})$. So what is the reason this isn't the case?