How was His Chesed great on David?
Radak #1: He saved David several times from his enemies and from Sha'ul, who sought to kill him.
Radak #2: He will save him.
Malbim: This refers to bodily benefits.
How was he saved from "She'ol Tachtis"?
Rashi: Adulterers are generally in the depth of Gehinom. You saved me, for Nasan ha'Navi told me "Gam Hashem He'evir Chatascha" (Shmuel II, 12:13).
Radak #1: He was saved from the grave (death). "Tachtis" merely repeats the affliction; every She'ol (pit) is Tachtis! Rather, it increases [the depth], like "b'Imkei She'ol Keru'eha" (Mishlei 9:18).
Radak #2: This refers to the future. Past tense is often used in place of future in Nevu'ah.
Radak #3: It is from the judgment of Gehinom.
Malbim: This refers to benefit of the Nefesh. He saved the Nefesh from the Yetzer ha'Ra and powers that would make it sin.