Free Derivative Worksheet PDF: Practice Problems with Answer Keys

Master higher order derivatives with 85 rigorous practice problems — from second derivatives to nth order, including motion analysis, concavity, and real-world modeling. Full step-by-step solutions, AP & university level.

Master the Power Rule, Constant Rule, and Sum Rule for derivatives with 65 practice problems, complete step-by-step solutions, worked examples, and real-world applications. Ideal for AP Calculus AB/BC, university Calculus I students.

Master d/dx[x^n] = n·x^(n-1) with 25 targeted problems covering polynomials, negative exponents, and fractional exponents. Complete step-by-step solutions included. The essential foundation for all derivative work.

Master the Chain Rule for derivatives with 80 practice problems, complete step-by-step solutions, worked examples, and real-world applications. Ideal for AP Calculus AB/BC, university Calculus I & II students.

A comprehensive worksheet on the limit definition of the derivative — 70+ problems, full solutions, worked examples, and real-world applications.

A dominant, publication-ready worksheet on implicit differentiation with 75+ problems, full solutions, worked examples, and modeling applications.

Deepen your understanding of average rate of change through 80+ scaffolded problems, full solutions, and real‑world modeling. Perfect for AP Calculus and university prep.

Master the Quotient Rule for derivatives with 67+ practice problems, complete step-by-step solutions, worked examples, and real-world applications in physics, engineering, and economics. Ideal for AP Calculus AB/BC and university students.

Master the Product Rule for derivatives with 75+ original problems, full solutions, and real‑world applications. Perfect for AP Calculus, college Calculus I, and engineering prep.

Build confidence with the constant rule and constant multiple rule — the essential foundation before tackling complex derivatives. Great for beginners and students reviewing fundamentals.

Combined practice with constants, power rule, and basic polynomial functions. Perfect for beginners building foundational skills and preparing for their first derivative test.

Comprehensive practice with (uv)' = u'v + uv'. Covers polynomial products, trigonometric products, and exponential products — each with detailed step-by-step solutions and worked examples.

Apply (u/v)' = (u'v − uv')/v² with confidence. Covers rational functions, trigonometric quotients, and mixed expressions. Each problem solved with full working shown.

Practice derivatives of sin, cos, tan, cot, sec, and csc with memory aids and pattern recognition exercises. A must-complete worksheet before tackling calculus limits and continuity problems.

Master e^x, ln(x), and general base functions — the building blocks for limits involving L'Hôpital's rule. Covers natural exponential, natural log, and general base derivatives with detailed solutions.

Test your mastery! Problems require you to decide which rule(s) to apply — just like on a real AP Calculus exam. Combines product, chain, and quotient rules across 35 challenging problems.

Combine trigonometric derivatives with chain rule for high-frequency AP Calculus problem types. Covers sin(3x²), cos(x³), tan(√x), and nested compositions that regularly appear on AP exams.

Find dy/dx for equations not explicitly solved for y. Covers circles, ellipses, hyperbolas, and complex implicit relationships. Includes full step-by-step solutions for every problem.

Real-world derivative applications! Minimize costs, maximize areas, and solve practical engineering and business scenarios. Critical for AP Calculus AB and college calculus exams.

Tackle classic related rates problems: expanding circles, filling cones, sliding ladders, and shadow problems. Builds the deep conceptual understanding that separates B students from A students in AP Calculus.

Free K‑2 math worksheet: build number sense with counting, writing numbers, addition & subtraction within 20, place value, and simple word problems. Complete with step-by-step solutions.