Basic Derivative Rules Worksheet | Differentiation Practice with Answer Key

A worksheet on basic differentiation rules:

• constant rule
• power rule
• constant multiple rule
• sum and difference rules
• product rule
• quotient rule
  There are 24 problems. Detailed solutions are included.

Equip your sixth-form mathematics students with this comprehensive, classroom-ready practice packet! Designed specifically for AS/A-Level Core Maths, Further Maths, or early university-level students, this resource features a robust set of comprehensive differentiation questions complete with full, step-by-step worked solutions.

Whether you need a targeted homework task, an in-class practice workshop, a revision lesson before exams, or a dependable assessment, this packet provides a seamless way to build student confidence with finding rates of change and manipulating algebraic expressions.

What is Included?

• Multi-Step Practice Questions: A wide variety of functions that naturally progress from simple powers to complex algebraic expressions.
• Full Step-by-Step Worked Solutions: Comprehensive algebraic breakdowns for every single question, making marking a breeze or allowing students to self-assess effectively.
• Versatile Layout: Cleanly organized layout with boxes that give students plenty of dedicated space to write out their working and derivative notation.

Core Concepts Covered

• Applying the Constant Rule and Power Rule for single terms.
• Utilizing the Sum and Difference Rules to differentiate long polynomials.
• Using the Product Rule and Quotient Rule to handle multiplying or dividing expressions.
• Rewriting radicals into rational fractional indices before differentiating.
• Moving variables out of denominators using negative indices.
• Fully simplifying final derivatives with clean algebraic manipulation.

Perfect For:

• Daily Homework or Independent Learning Tasks
• Small-Group Intervention & Calculus Remediation
• End of Topic Assessment & Exam Revision
• Quick and Easy Emergency Cover Plans

Curriculum Alignment

• AS and A-Level Mathematics: Directly targets core algebraic manipulation, understanding the derivative as a rate of change, and applying fundamental rules of differentiation to combinations of polynomial functions.