What do you recommend instead? y'? y_x? Newton's dot notation?

A notation which I find quite helpful in my rough notes - but is completely non-standard - is "f ≡> g" for "g is the derivative of f". The reason this is helpful is because you can write out a big expression, decide you need to differentiate it, and then carry on doing just that without needing to copy it out or introduce a name for it.