JEE Differentiation Quiz
Chapter-wise practice on the rules of differentiation, chain rule, implicit and parametric differentiation, and applications to tangents, maxima and minima.
Skill map
Levels in this jee differentiation quiz
Every question is generated fresh by AI and calibrated to your level - clear a level and the next one gets harder. Miss one and the AI tutor explains Differentiation until it sticks, then aims a follow-up at the gap. Want to grind one level? Start the quiz and type that sub-topic as your own.
Exam focus
How Differentiation is asked
Together with Integration, this is the largest block in JEE Mathematics. Applications of derivatives - tangents, monotonicity, maxima and minima - are asked more often than raw differentiation, so practice should weight the applications correspondingly.
Cheat sheet
Differentiation formulas worth memorising
| Quantity | Formula |
|---|---|
| Product rule | (uv)′ = u′v + uv′ |
| Quotient rule | (u/v)′ = (u′v − uv′)/v² |
| Chain rule | dy/dx = (dy/du)(du/dx) |
| Parametric form | dy/dx = (dy/dt)/(dx/dt) |
| Slope of tangent | dy/dx at the point |
| Slope of normal | −1 / (dy/dx) |
| Critical points | f′(x) = 0 or f′ undefined |
| Second derivative test | f″ > 0 minimum, f″ < 0 maximum |
Marks lost here
Common mistakes in Differentiation
- Getting the quotient rule the wrong way round. The numerator is u′v − uv′, and reversing it flips the sign of every answer that follows.
- Forgetting the inner derivative in the chain rule. Differentiating sin(3x) gives 3cos(3x), not cos(3x) - the most frequent single error in the whole chapter.
- Testing only f′(x) = 0 for extrema. Critical points also occur where the derivative is undefined, and endpoints must be checked separately on a closed interval.
- Assuming f″(x) = 0 means a point of inflection. The second derivative must actually change sign there; x⁴ has f″(0) = 0 at a genuine minimum.
- Confusing the slope of the tangent with that of the normal. They are negative reciprocals, and questions often ask for one after giving information about the other.
Game rules
How a round works
- 01Spawn
Press play - the AI generates Differentiation questions in seconds.
- 02Level up
Answer to earn XP and build a streak. Difficulty adapts to your accuracy and speed.
- 03Learn or lose
Every answer - right or wrong - gets an AI tutor explanation. Wrong answers respawn as follow-ups.
Leaderboard
Differentiation high scores
Next challenges
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Player's guide
JEE Differentiation Quiz - FAQs
When should I use logarithmic differentiation?
When the variable appears in the exponent, as in x^x, or when a function is a long product or quotient. Taking logarithms first turns products into sums and exponents into coefficients, which is usually far quicker than repeated product-rule application.
How do I find the absolute maximum on a closed interval?
Evaluate the function at every critical point inside the interval and at both endpoints, then compare the values. The second derivative test identifies local behaviour only - it cannot tell you about the endpoints, which is where the absolute extremum often is.
Is the jee differentiation quiz free?
Yes - completely free, with no sign-up required. Type a topic, press start, and the AI generates an adaptive Differentiation quiz with an explanation for every answer.
Can teachers host this jee differentiation quiz live for a class?
Yes - create a free teacher account, host a live room on "Differentiation", and students join with a 6-character code at quff.in/join. No student accounts needed.
From the blog
Differentiation guides & reading
JEE Differentiation: 30 Practice Questions with Solutions
Thirty solved Differentiation questions, weighted toward applications of derivatives - which is where the paper actually puts its marks.
Exam PrepJEE Limits: 30 Practice Questions with Full Solutions
Thirty solved Limits questions, starting from the check that decides the method: is the form actually indeterminate?
Exam PrepJEE Integration: 30 Practice Questions with Solutions
Thirty solved Integration questions, organised around the only decision that matters: which technique the integrand is asking for.
More exam prep quizzes
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Six adaptive Differentiation questions. About two minutes. Climb the podium.