The question I would choose is: "What makes people live?" It was written about by Freud in Beyond the Pleasure Principle and built upon by Derrida in To Speculate--on "Freud", (in his book The Postcard). The concept also connects with Nietzsche's Will to Power.
Similarly, the phenomenon that Heidegger placed in this central role is Sorge (Care), however Derrida's refined 'Life Drive' is deeper and more unconscious than Sorge.
"For Heidegger, it is Sorge that signifies a man's existence and makes
it meaningful. To be-in-the-world in an authentic existential pretext
is to be 'careful'. Heidegger concluded that 'care' is the primordial
state of Being as Dasein strives towards authenticity (Steiner 1978)."
quoted from: What Heidegger Means by Being-in-the-World
Here is a pertinent quote from To Speculate--on "Freud". It's rather difficult to put Derrida's thesis in a nutshell because in the essay he has built up a multithreaded framework by the time he draws conclusions. Nevertheless, some flavour :-
"Now, if such a drive for power exists, if it sees itself attributed a
specificity, then it indeed has to be admitted that it plays a very
original role in the most "meta-conceptual," "metalinguistic,"
precisely the most "dominant" organization of Freudian discourse. For
it is indeed within the code of power, and this is not only
metaphorical, that the problematic is lodged. It is always a question
of knowing who is the "master," who "dominates," who has "authority,"
to what point the PP [pleasure principle] exercises power, how a drive
can become independent of it or precede it, what are the relations of
service between the PP and the rest, what we have called the prince
and his subjects, etc. The "posts" are always posts of power. And
power is exercised according to the network of posts. There is a
society of drives, whether or not they are communally possible, and in
the passage to which we have just referred (chapter VI), the dynamics
of sadism are dynamics of power, dynamics of dynasty: a component
drive must come to dominate the entirety of the body driven, and must
subject this body to its regime; and if this suceeds, it is with the
aim of exercising the violence of its domination over the object. And
if this desire to dominate is exercised within as well as without, if
it defines the relation to oneself as the relation to the other of the
drives, if it has an "original" root, then the drive for power can no
longer be derived. Nor can postal power. In its autoheterology, the
drive for postal power is more originary than the PP and independent
of it. But it equally remains the only one to permit the definition
of a death drive, and for example an original sadism. In other words,
the motif of power is more originary and more general than the PP, is
independent of it, is its beyond. But it is not to be confused with
the death drive or the repetition compulsion, it gives us with what to
describe them, and in respect to them, as well as to a "mastery" of
the PP, it plays the role of transcendental predicate. Beyond the
pleasure principle—-power. That is, posts. But even so, we will not
say, despite the transcendental function to which we have just
alluded, beyond the death drive-—power—-or posts. For it is equally
the case that everything described under the heading of the death
drive or the repetition compulsion, although proceeding from a drive
for power, and borrowing all its descriptive traits from this drive,
no less overflows power. This is simultaneously the reason and the
failure, the origin and the limit of power. There is power only if
there is a principle or a principle of the principle. The
transcendental or meta-conceptual function belongs to the order of
power. Thus there is only différance of power. Whence the posts.
Beyond all conceptual oppositions, Bemächtigung indeed situates one of
the exchangers between the drive to dominate as the drive of the
drive, and the "will to power.""
(The Postcard, 1987, pages 404-405)
One might ask how Life Drive, Death Drive and Will to Power can be the same thing, and how they can be likened to Sorge (Care), but fundamentally this is what drives beings: a facility to be careful; gain mastery over environment; antisocially, to dominate. Hence Life Drive can become Death Drive. Problem solving tenacity can also be frustrated into repetition compulsion. This drive fundamentally lies at the heart of existential phenomenology, and at the core of individual and social creativity and destructivity.