Scales to Play Over Dadd9
Every chord is a subset of several scales: any scale that contains all of a chord's tones fits over it. Pick a chord to see the matching scales from its own root, the major keys the chord belongs to, and full fretboard diagrams for every scale on guitar.
A Dadd9 chord contains the notes D – E – F# – A. Any scale that includes every one of those 4 tones fits over it — from the root D, that means D Major, D Major Pentatonic, D Rock 'n' Roll, D Lydian, D Mixolydian, D Dorian Bebop and D Mixolydian Bebop. Start with the first scale listed: it is the most common choice, and the others color the same chord tones differently.
Dadd9 is also diatonic to 3 major keys: A major (relative minor F#m), D major (relative minor Bm), G major (relative minor Em). In a song from one of those keys you can also solo with the key's own major scale or its relative minor pentatonic across the whole progression, not just this chord.