Psalm 75:9, "But I will declare this forever: I will sing praises to the God of Jacob," expresses a deep and lasting commitment to publicly acknowledge and worship God. Let's break down the meaning:

"But I will declare this forever:" This signifies a resolute and unwavering decision. The speaker is making a vow, a promise that they will not waver in their devotion. The word "forever" implies a commitment that extends throughout their life and potentially even beyond.

"I will sing praises to the God of Jacob:" This indicates the specific form of worship the speaker will engage in. Singing praises is an act of joyful and thankful adoration. "The God of Jacob" is a specific title for the God of Israel, harking back to the patriarch Jacob (Israel) and the covenant God made with him and his descendants. It emphasizes God's faithfulness to His promises to the nation of Israel. It also could be a specific reference to God's character.

Overall Meaning:

The verse is a statement of unwavering faith and commitment to God. It is a vow to consistently and publicly acknowledge God's goodness and power through songs of praise. The speaker is not simply expressing a temporary sentiment but making a lifelong declaration of loyalty and worship to the God who has shown Himself faithful to Jacob (Israel).

In essence, it is a promise to:

Publicly acknowledge God: The speaker is not shy about their faith; they will openly declare it.
Worship God through song: Music is a powerful tool for expressing devotion and gratitude.
Remain faithful to God: The commitment is for a lifetime, a promise not to abandon their faith.
Remember God's covenant with Israel: By referring to "the God of Jacob," the speaker acknowledges God's historical relationship with the Jewish people.

The verse can be a source of inspiration for believers to reaffirm their commitment to worship and serve God faithfully throughout their lives.