Learn differentiation by doing it, one step at a time.
Every rule starts with the idea behind it, then a fully worked method, then practice questions you can check your own working against, from foundational fluency up to exam style critical thinking. No typing required. Work it out on paper, then reveal each step to check yourself.
Start here
The Big Idea
Why the product rule and chain rule exist, told as two short stories: a growing garden bed and a rising weather balloon, with the real-world implications of each.
Read the story →Rule 1 of 3
Product Rule
The method laid out step by step, then ten foundational practice questions running from simplest to most involved.
Learn and practice →Rule 2 of 3
Chain Rule
The method and foundational practice for differentiating composite functions, plus a set of harder critical-thinking questions.
Learn and practice →Rule 3 of 3
Quotient Rule
Why the quotient rule is really the product rule in disguise, then the method, practice, and harder questions.
Read the story →Lesson 4
Second Derivatives & Curve Sketching
Concavity, points of inflection, the second derivative test, and sketching a graph from its derivatives.
Read the story →Lesson 5
Applications: Rates & Optimisation
Kinematics (velocity and acceleration), optimisation problems from many fields, and the increments formula for estimating small changes.
Read the story →Lesson 6
Gradients From Graphs
Reading gradients off a graph, applying the product and chain rules at a point from graphed values alone, and sketching f′ from f or f from f′. Twenty practice questions, ten harder ones, and a ClassPad guide.
Read the story →