These two psalms are linked together by an Acrostic which is irregular and broken, just like the troubled times which both of these psalms address. This Acrostic tells us that the subject of the two Psalms is one and that they are to be connected together. From 9:1 to 10:17, each line of each Psalm starts with a letter in the Hebrew alphabet, and they each appear in order, except for the third letter, the gimmel, and there are 3 letters missing, but the rest of the alphabet is used in order. Psalm 9 is written with a note as authored by David, whereas 10 is not noted, like an addendum added by the same author, but written at a later date. Many theology scholars explain this by defining “Muth-labben” (the tune psalm 9 is to be sung with) meaning “the death of the man who went out between camps”. This word is used of Goliath in 1st Samuel 17:4. So it’s plausible David wrote Psalm 9 soon after the incident of killing him and he could have written Psalm 10, much later upon reflection on one of his last battles with the Philistines mentioned in 2nd Samuel 21:15. Whatever the case, it is referenced in the New Testament, See Romans 3:9-20, as verse14 is where Paul quotes from Psalm 10:7, Why? Because the nature of sin that we all explore and experience is exactly what God’s enemies live like. Both of these Psalms are praising God for his eventual victory over the enemies of God’s children.
The deeds David refers to here in 9:11 are likely the wonderful acts the Lord performed on behalf of Israel (Psalm 9:1–6). This might have implied His deliverance of His people from Egypt and His miraculous provisions for them in the wilderness. However, the actions in question might be more personal: what God has done in the lives of the oppressed. Christians today should declare how much God has done for them (Luke 8:39; 1 Peter 2:9–10; 3:15; Romans 10:14–15) in spite of our failings with sin or problems or discipline. Praise God!
Psalm 9:13 has the term “the gates of death” found in Job 38:17, Psalm 107:18, and Isaiah 38:10. It echoes the idea of death as crossing some barrier or border, from which there is no escape until the resurrection. David believed the Lord could and would preserve his life. Believers need not fear death, because it ushers them into the presence of the Lord (2 Corinthians 5:8). The apostle Paul regarded death, for the Christian, as gain (Philippians 1:21).
Psalm 10 reflects the natural frustration we feel in the face of evil. In our limited understanding, we cannot grasp why God is not intervening right here, right now, and in exactly the way we’d prefer. As with other Old Testament passages, the psalmist later returns to the idea of God’s established faithfulness, but the initial cry of his heart is one of a disturbed spirit. Though the passage began with a sense of frustration and anguish, it ends with a hopeful, faithful tone. What God has accomplished for His people produces confidence: a trust that He will hear and act according to His perfect goodness.