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Differentiation — JEE Practice

30 practice questions across 2 topics. Filter by difficulty, solve topic-wise MCQs, and review detailed solutions.

2 Topics30 Questions

Derivatives & Rules(15 Qs)

easy (5)

Q1d/dx(xⁿ) =Q2d/dx(sin x) =Q3d/dx(eˣ) =Q4The product rule states d/dx(uv) =Q5d/dx(ln x) =

medium (5)

Q1d/dx(tan x) =Q2Chain rule: d/dx[f(g(x))] =Q3d/dx(x²sin x) by product rule =Q4If y = sin⁻¹(x), then dy/dx =Q5Quotient rule: d/dx(u/v) =

hard (5)

Q1If y = xˣ, then dy/dx =Q2The nth derivative of eᵃˣ is:Q3If f(x) = |x|, then f'(0) is:Q4For implicit differentiation of x² + y² = 25, dy/dx =Q5d/dx(tan⁻¹(x)) =

Applications of Derivatives(15 Qs)

easy (5)

Q1The slope of tangent to y = f(x) at x = a is:Q2If f'(x) > 0 on an interval, f is:Q3At a local maximum, f'(x) =Q4Rate of change of area of circle w.r.t. radius is:Q5The equation of tangent to y = x² at (1,1) is:

medium (5)

Q1For maxima, the second derivative test requires:Q2Rolle's theorem requires:Q3The maximum value of f(x) = x(1-x) on [0,1] is:Q4If a spherical balloon inflates at 4π cm³/s, rate of radius increase when r = 2 cm is:Q5LMVT states: if f is continuous on [a,b] and differentiable on (a,b), then:

hard (5)

Q1The minimum value of f(x) = eˣ + e⁻ˣ is:Q2The function f(x) = x³ - 3x has point of inflection at:Q3The shortest distance from origin to curve y = eˣ/√2 is:Q4A rectangle inscribed in a circle of radius r has maximum area:Q5Using Newton's approximation, the root near x₀ is:

More Mathematics Chapters

Sets, Relations & Functions

15 Qs

Complex Numbers

15 Qs

Quadratic Equations

15 Qs

Permutations & Combinations

15 Qs

Binomial Theorem

15 Qs

Matrices & Determinants

15 Qs

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