Introduction:
When studying mathematics or any other subject, it is important to strike a balance between understanding the derivations and proofs and focusing on their applications. Both aspects are crucial for a comprehensive understanding of the subject. Let's discuss the importance of each and how they complement each other.

Understanding Derivations and Proofs:
1. Building foundational knowledge: Derivations and proofs provide the foundation of mathematical concepts and theories. They help you understand the underlying principles and logic behind the applications.
2. Strengthening problem-solving skills: By revising derivations and proofs, you develop analytical thinking and problem-solving skills. It enables you to tackle complex problems by breaking them down into smaller steps.
3. Enhancing critical thinking: Studying derivations and proofs challenges your critical thinking abilities. It encourages you to question assumptions, analyze arguments, and develop a deeper understanding of mathematical concepts.

Understanding their Applications:
1. Real-world relevance: Understanding the applications of derivations and proofs helps you appreciate the practical significance of mathematical concepts. It enables you to apply them to real-world scenarios, such as engineering, physics, economics, or computer science.
2. Connecting theory with practice: Applications provide a bridge between theoretical knowledge and practical problem-solving. By focusing on applications, you can see how mathematical concepts can be used to solve problems and make informed decisions.
3. Improving retention and engagement: Learning the applications of derivations and proofs makes the subject matter more relatable and engaging. It helps you remember and apply the concepts better, as you can visualize their usefulness in various contexts.

The Importance of Balance:
To truly understand a subject, it is important to strike a balance between revising derivations and proofs and focusing on their applications. Here's why:
- Comprehensive understanding: A deep understanding of a subject comes from knowing the theory behind it as well as its practical applications.
- Effective problem-solving: By understanding both derivations and applications, you can approach problem-solving from different angles and choose the most appropriate method.
- Flexibility in learning: Some individuals may find derivations and proofs more interesting, while others may prefer applications. By balancing both, educators can cater to a wider range of learning styles and preferences.

Conclusion:
In conclusion, revising derivations and proofs is essential for building a strong foundation and developing analytical skills. However, focusing on their applications is equally important to understand the practical relevance and foster engagement. Striking a balance between both aspects will lead to a comprehensive understanding of the subject and enable effective problem-solving in real-world scenarios.