What is true of it
D♯add9 is D♯, F𝄪, A♯ and E♯ — 1, 3, 5 and 9 counted from D♯.
F𝄪 is a double sharp, and it has to be: every letter from D♯ upwards is used once, so the 3 cannot be written any other way.
On an instrument that cannot reach all 4, the 5 goes first, in that order.
The easiest of the 1 fingering below is 8768: 4 fingers, held at the 6th fret.
None of them uses an open string, so this chord moves up the neck unchanged — the same shape 1 fret higher is the chord a semitone above.
Where its notes are on the neck
The brass dots are D♯, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
D♯add9/F𝄪
0311
D♯add9/A♯
3536
D♯add9/E♯
aaba
An inversion is the same chord with a different note lowest. The name changes to a slash name because the bass is what a listener hears as the foundation.