Large language models (LLMs) are impressive, but their size demands heavy computing power. What if we could make them smaller and more efficient without losing their smarts? That's the idea behind knowledge distillation (KD), a technique for training smaller "student" LLMs by transferring knowledge from larger, high-performing "teacher" LLMs. Traditional KD methods treat all data equally, but a new approach called DDK (Distilling Domain Knowledge) recognizes that LLMs have strengths and weaknesses in different subject areas or "domains." DDK dynamically adjusts the training data based on the student LLM's performance gaps in different domains. For example, if a student model struggles with medical terminology but excels at literary analysis, DDK feeds it more medical data. This targeted approach results in more efficient learning and better overall performance. Experiments show DDK significantly improves student LLM performance across diverse tasks, outperforming existing KD methods and even continuously pre-trained models. This means smaller LLMs can be trained to match the abilities of their larger counterparts, making them more accessible for various real-world applications. While there's still research to be done (fine-tuning parameters, experimenting with different model sizes), DDK offers a promising path toward smaller, smarter, and more resource-friendly LLMs.