Without a supply of formulae in our head we won't, in practice, be able to solve problems. The distinction is not clear cut. There are few formulae which have to be learned exactly. In many cases, it is sufficient to know that something of the sort exists and to have a way of reconstructing it when needed. And of course different people remember different things and in different ways.
Functions are positive in quadrants shown.
There are many more trigonometric formulae. One should know how to differentiate products of functions. One should also know how to differentiate functions of functions.