Playbook
Differentiation
141 q - 3.15/paper - 47% HARD. Method-pure subtopics, each drilling one technique. Inverse-trig differentiation (39 q) is the biggest single block. Derivative of One Function with respect to Another is only 7 q but 71% HARD - the worst marks-per-minute cell in the chapter.
- Questions in the bank
- 141
- q/paper (2024–25 shifts)
- 3.15
- Tagged HARD
- 47%
- Subtopics
- 6
Strand: Cornerstone
When you’ll see it
A derivative to be computed, where the shape of the function — implicit, parametric, logarithmic, inverse trigonometric — names the method before you start.
How this chapter is tested
141 q at 3.15 per paper and 47% HARD. The subtopics here are method-pure: each one drills exactly one technique, and the exam sets them the same way. That is good news, because it means the chapter is learnable in six discrete pieces rather than as one undifferentiated mass — but it also means the exam expects you to identify the method from the shape of the function within a few seconds.
Start with Foundations, Chain Rule and Differentiability (21 q, 29% HARD), which is the cheapest block and underlies all five others. Then Logarithmic Differentiation (25 q, 44%), which is a single trick applied consistently. Implicit Differentiation and Special Forms (31 q, 52%) and Parametric, Higher-Order Derivatives and Relations (18 q, 50%) come next. Inverse Functions and Inverse Trigonometric Differentiation is the biggest single block at 39 q and 49% HARD, and it deserves the most drilling time.
Derivative of One Function with Respect to Another deserves an explicit warning: 7 q at 71% HARD, the worst marks-per-minute cell in the chapter. That is fewer than one appearance in six papers, at the highest difficulty rate here. Learn it last, and if it turns up when the clock is short, mark an option and move on — MHT-CET has no negative marking, so an unanswered question and a wrong one cost exactly the same.
One measured overlap to plan around: inverse trigonometry appears BOTH as its own chapter (73 q) and as a subtopic inside Trigonometry - II (21 q), and its differentiation lives here. The pre-simplification step — recognising a standard substitution that collapses a monstrous inverse-trig expression into something linear — is usually the entire question, and it is a trigonometry skill, not a calculus one.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Foundations, chain rule, and differentiability
Product, quotient and chain rules applied without hesitation, plus the definition-based questions about where a function is differentiable. 21 q at 29% HARD — the cheapest block and the base for everything else.
Logarithmic differentiation
Take logarithms first when the function is a product of many factors or has a variable in the exponent, then differentiate implicitly. 25 q at 44% HARD. One trick, applied the same way every time.
Implicit differentiation and special forms
Differentiate both sides with respect to x, attaching the derivative factor to every y term, then solve for it. 31 q at 52% HARD, the second-largest block.
Parametric, higher-order derivatives, and relations
Divide the two parameter derivatives for the first derivative; for the second, differentiate that result with respect to the parameter and divide again. 18 q at 50% HARD, and the second-derivative step is where most of the difficulty sits.
Inverse functions and inverse trigonometric differentiation
Simplify the inverse-trigonometric expression with a substitution BEFORE differentiating. 39 q at 49% HARD — the largest single block in the chapter, and the simplification is usually the whole question.
Derivative of one function with respect to another
Differentiate both functions with respect to the shared variable and take the ratio. 7 q at 71% HARD: the worst marks-per-minute cell in the chapter, so it goes last in the learning order.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the patterns that cut across chapters.
Chain factor dropped on a composite
Differentiating the outer function correctly and forgetting the inner derivative. The result is a clean expression that is present in the options, which is what makes it convincing.
Implicit derivative missing on a y term
Treating y as a constant partway through. Every y that gets differentiated must carry the derivative factor — including inside products and powers.
Variable base and variable exponent handled as one rule
A function with a variable in both base and exponent is neither a power rule nor an exponential rule case. Both single-rule answers appear as distractors; logarithmic differentiation is the only correct route.
Second parametric derivative taken as a ratio of second derivatives
The second derivative is not the ratio of the two second parameter derivatives. It requires differentiating the first result and dividing by the parameter derivative again.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a per-subtopic mastery checkpoint. Read the notes once, then drill subtopic by subtopic below.
Differentiation notesDrill every differentiation question
141 questions from the bank, scoped to 6 bundled subtopics.
Drill one subtopic at a time
The 6 subtopics this playbook covers, in catalog order.
Related playbooks
Often paired with this one — the technique, the trap or the taxonomy overlaps. Drill these next.