Why does $TdS = d(TS)$ for constant T? For an isothermal process, (T remains constant) we can say that $Tds = d(TS)$. How can this be correct? Isn't $d(TS) = 0$ if T is constant?

$\ d(TS)=TdS+SdT$

So if $\ T$ is constant, you have $\ dT=0$ and the result follows