PPT Lesson 2 - Derivative (First Principles) - harder

Lesson 2 Derivatives from First Principles – Cubic and Quartic Functions

This is the second lesson in the Derivatives from First Principles series, focusing on applying the first principles method to cubic and quartic functions. The resource is ideal for high-attaining students who are already confident with algebraic expansion and factorisation, and who are ready to extend their understanding of calculus into more complex expressions.

Resource Overview

This download includes:

Editable PowerPoint presentation (24 slides)

Covers the application of the first principles formula to cubic and quartic functions

Step-by-step worked examples to model the process

Carefully structured animations for smooth, teacher-led delivery

Includes introduction and conclusion slides to frame the lesson

Sample slides: 2, 4, 9, 14, and 20 are included for preview

Two printable PDF worksheets - each with 10 progressively challenging questions (20 total)

Focus on algebraic expansion, collecting like terms, and factorising expressions as needed

One fully worked example included per worksheet

Fully worked solutions

Complete step-by-step solutions provided in a separate document

Learning Objectives

By the end of this lesson, students will be able to:

Extend their use of the first principles method to cubic and quartic functions

Apply algebraic techniques such as expansion and factorisation within the context of calculus

Develop fluency with complex expressions and algebraic manipulation

Strengthen their conceptual grasp of what differentiation means from a foundational level

Teacher Guidance

The PowerPoint slides are fully editable and animated for classroom delivery

Worksheets are ideal for classwork, homework, or revision

Designed for confident students – this lesson assumes strong prior knowledge of basic differentiation from first principles and algebraic fluency

This resource does not include teacher notes or video instruction. If you are seeking a complete video lesson covering the same topic (with worksheets and solutions included), please browse the full video-based resource available in my TES shop.

File Formats

PowerPoint (.pptx) – fully editable

Worksheets and solutions (PDF) – ready to print or distribute digitally

Related Resources

This is Lesson 2 in the Derivatives from First Principles series. For earlier lessons or a bundled version with video content, please visit my TES shop for the full unit.