This is not a differential, but a derivative; they are different things. Since f' denotes the derivative of f, which is a function of its own, the best notation for the value at 1 is
If you want to use the heavier notation
is perfectly good. You may want to define a command for this:
to be used as
or, if you need a larger bar to cover a larger function symbol,
The optional argument can be one of
\Bigg. I wouldn't use an automatically growing bar, because it may give bad results.