Derivatives of Exponential Functions Worksheet & Answer Key | AP Calculus

A worksheet on differentiating exponential functions. Detailed solutions are included.

Master differentiating exponential functions with this comprehensive, print-and-go A-Level Mathematics resource! Perfect for Year 13 Pure Maths students, this activity contains 24 carefully scaffolded questions complete with a step-by-step, fully worked mark scheme. Help your students build confidence using base-e, alternative bases, chain rule, product rule, and quotient rule applications.

Save time planning and give your students the exact practice they need to master the calculus of exponential functions!
This ready-to-print resource features 24 carefully curated questions designed to take students from foundational index and exponential rules to advanced differentiation techniques. It covers standard natural exponential functions (e^x) as well as arbitrary bases (such as base 2, 5, and 7), seamlessly blending in the chain, product, and quotient rules. Whether you are looking for a rigorous homework assignment, independent revision, or a structured in-class activity, this pack has you covered.

What’s Included:
• 24 High-Quality Questions: Covers basic exponential derivatives, arbitrary bases (such as 2^x, 7^x, and 5^x), negative and fractional exponents, trigonometric combinations, and complex products.
• Fully Worked Mark Scheme: A comprehensive, step-by-step breakdown of solutions is provided for every single question—perfect for quick teacher assessment or independent student self-checking!
• Clean, Organized Layout: Clearly structured questions give students an excellent framework to organize their mathematical working.

Curriculum & Exam Board Alignment:
• A-Level Mathematics (Year 13): Explicitly maps to the calculus, differentiation rules, and exponential functions criteria across all major UK exam boards including Edexcel, AQA, OCR, and OCR MEI.
• Advanced Higher / International Baccalaureate (IB): Ideal for higher-level analysis, calculus techniques, and mathematical methods.

Ways to Use This Resource in Your Classroom:
• Independent Homework: Reinforce your daily lesson with targeted skill practice.
• Revision & Exam Prep: Excellent for structured unit reviews ahead of mocks or final A-Level examinations.
• Collaborative Group Work: Perfect for getting students to pair up, solve, and compare their differentiation steps.
• Cover Lessons: Clear layouts and a complete step-by-step mark scheme make this an incredibly low-maintenance resource to hand over for a cover class.