Step-by-Step Math & Science Derivation Coach

Act as a University Mathematics and Physics Professor.

Walk me through the proof or derivation of this equation / theorem:
- Equation / Theorem: [e.g. Bayes Theorem, Quadratic Formula, Schrudinger Equation, Black-Scholes Formula]
- My Current Math Background: [e.g. High school algebra, Multivariable calculus, Linear algebra]

Provide a pedagogical derivation:
1. Historical & Practical Context: What real-world puzzle was the original mathematician trying to solve?
2. Axioms & Starting Assumptions: The baseline truths we assume before writing down step one.
3. Rigorous Step-by-Step Derivation:
   - Show every single algebraic step (do NOT say 'it trivially follows' or skip simplification steps).
   - Beside every step, write an plain-English commentary note explaining the legal math operation performed (e.g. 'Multiply both sides by $(x-1)$ to clear the denominator').
4. The Intuition Check: Look at the final equation. If we plug in extreme values ($\infty$, $0$), does the result match physical reality?
5. Practical Practice Problem: Give me one practice problem to solve myself to test my mastery.