Should You Memorise Derivations or Just Formulas?

Short answer: yes, learn the derivations. Not because every one is asked in the exam, but because derivations are the cheapest way to prevent formula errors.

Three reasons to learn derivations

1. Direct mark reward

CBSE Class 12 Physics board paper has derivation questions almost every year:

• 3 marks: Derive E = -\frac{dV}{dr}.
• 5 marks: Derive Biot–Savart law application to a solenoid.
• 5 marks: Derive lens formula.
• 3–5 marks: Derive expression for capacitance of parallel-plate capacitor with dielectric.

If you memorised the formula but not the derivation, you lose 5–10 marks in each paper.

2. Formula reconstruction under pressure

Exam pressure makes you forget. If you know the derivation, you can rebuild the formula from memory:

Forgot \int \frac{1}{x^2 + a^2} dx = \frac{1}{a} \tan^{-1}\frac{x}{a} + C?

Substitute x = a \tan\theta, dx = a \sec^2\theta d\theta. Denominator = a^2 \sec^2\theta. Integral becomes \int \frac{1}{a} d\theta = \frac{\theta}{a}. Substitute back — you have the formula.

30 seconds and no memorisation needed.

3. Avoiding wrong signs

• E = -\frac{dV}{dr}: the minus sign is derived, not arbitrary.
• Faraday's law \varepsilon = -\frac{d\Phi}{dt}: minus sign = Lenz's law direction.
• Beer-Lambert \log(I_0/I) = \varepsilon c l: log base 10, not natural log.

Every one of these has a "forgot the sign" trap that a derivation would have caught.

Which derivations are MUST-know

Rank of importance for CBSE Class 12:

| Chapter | Derivation | Priority | |---------|-----------|----------| | Physics | Coulomb's law application → Gauss | ★★★★★ | | Physics | Motional EMF two ways (force + flux) | ★★★★★ | | Physics | Bohr's radius r_n ∝ n² | ★★★★☆ | | Physics | Parallel-plate capacitor energy | ★★★★☆ | | Physics | Reflection of ray at plane mirror | ★★★☆☆ | | Chemistry | Nernst equation from ΔG | ★★★★★ | | Chemistry | Rate constant from Arrhenius | ★★★★☆ | | Maths | Integration by parts from product rule | ★★★★★ | | Maths | Sum of AP/GP | ★★★★☆ | | Maths | Bayes theorem | ★★★★☆ | | Biology | Hardy-Weinberg | ★★★★☆ | | Biology | Dihybrid 9:3:3:1 ratio | ★★★★★ |

Which derivations you can skip

• Full quantum-mechanical derivation of Bohr's model (Class 12 needs conceptual understanding, not the QM math).
• Rigorous proof of the fundamental theorem of calculus (application-focused syllabus).
• Full protein-synthesis mechanism at the enzyme level (only the flow matters).

How Board Formulas helps

Every formula on Board Formulas has a click-to-reveal "Why this formula?" derivation. Read it once, close it. Do this for each formula in a chapter and your understanding becomes permanent.

Memorising the formula alone is a shortcut that costs you in the exam. Learn derivations — it's the cheapest defence you have.