Differentiation runs through Continuity and Differentiability, Application of Derivatives and even Integration. Keep this list in your notebook and you cover three chapters at once.
Standard derivatives
- d/dx(xⁿ) = nxⁿ⁻¹; d/dx(c) = 0
- d/dx(eˣ) = eˣ; d/dx(aˣ) = aˣ ln a; d/dx(ln x) = 1/x; d/dx(logₐx) = 1/(x ln a)
- d/dx(sin x) = cos x; cos x → −sin x; tan x → sec²x; cot x → −cosec²x; sec x → sec x tan x; cosec x → −cosec x cot x
- d/dx(sin⁻¹x) = 1/√(1 − x²); cos⁻¹x → −1/√(1 − x²); tan⁻¹x → 1/(1 + x²); cot⁻¹x → −1/(1 + x²); sec⁻¹x → 1/(|x|√(x² − 1))
Rules
- Product: (uv)′ = u′v + uv′
- Quotient: (u/v)′ = (u′v − uv′)/v²
- Chain rule: d/dx f(g(x)) = f′(g(x)) g′(x)
Methods
- Implicit: x² + y² = 25 → 2x + 2y y′ = 0 → y′ = −x/y
- Parametric: dy/dx = (dy/dt)/(dx/dt). x = a cos t, y = a sin t → dy/dx = −cot t
- Logarithmic: y = xˣ → ln y = x ln x → y′/y = ln x + 1 → y′ = xˣ(1 + ln x)
- Inverse trig simplification: tan⁻¹(2x/(1 − x²)) = 2 tan⁻¹x → derivative 2/(1 + x²)
Examples
1. y = sin(x²): y′ = 2x cos(x²).
2. y = e^(3x) ln x: y′ = 3e^(3x) ln x + e^(3x)/x.
Stuck on a question? Ask it here and get a step-by-step answer in seconds — pay only per answer, no subscription. Ask your doubt now →
3. y = √(1 + x²): y′ = x/√(1 + x²).
4. If y = A cos x + B sin x, show y″ + y = 0: y″ = −A cos x − B sin x = −y. ✓
Common mistakes
- Forgetting the inner derivative in the chain rule
- Sign errors in cos and cosec derivatives
- Not taking log before differentiating xˣ-type functions
Related: Integration formulas.
Stuck on a derivative question?
Type the exact question (or attach a photo), choose your class or exam and your language — Hindi, Hinglish, English or 9 more — and ask your doubt on DoubtPay AI. You get step-by-step working with a labelled diagram where it helps, and you can ask for a hint, an attempt check, practice questions or flashcards instead. No subscription: packs start at ₹9 for 15 answers, unused credits stay in your account.
Frequently asked questions
Are these Differentiation Formulas Class 12 notes enough for the exam?
They cover every formula, definition and question type that appears in school and board papers for this chapter. Use them with the NCERT examples, exercise questions and the last five years' papers to be fully prepared.
How should I revise Differentiation Formulas Class 12?
Revise the notes after 1 day, 7 days and 30 days. Solve five questions each time instead of only reading, and keep an error list of the steps you get wrong.
What if I get stuck on a differentiation formulas question?
Type or photograph the exact question on DoubtPay AI, choose your class and language, and get a step-by-step answer with a diagram. You can also ask for a hint or have your own attempt checked. Packs start at ₹9 for 15 answers.
Stuck on a question? Ask it here and get a step-by-step answer in seconds — pay only per answer, no subscription. Ask your doubt now →