# Differential Calculus notes

> CAPS-aligned study notes for Differential Calculus in Grade 12 Mathematics. Browse the sections below for explanations, worked examples and exam preparation.

- Page: https://www.hlayiso.com/grade-12/mathematics/notes/differential-calculus

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## Sections in Differential Calculus

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- [Average Gradient](https://www.hlayiso.com/grade-12/mathematics/notes/differential-calculus/average-gradient) — Average Gradient In Grade 10 and 11, you worked with the gradient of a straight line. You learnt that a straight line has a constant gradient everywhere. But what happens when you need to find the…
- [Average Rate of Change](https://www.hlayiso.com/grade-12/mathematics/notes/differential-calculus/average-rate-of-change) — Average Rate of Change You already know how to calculate the average gradient between two points on a curve. In this section, you will see that the same calculation has a powerful real-world…
- [The Derivative of a Function at a Point](https://www.hlayiso.com/grade-12/mathematics/notes/differential-calculus/the-derivative-of-a-function-at-a-point) — The Derivative of a Function at a Point In the previous sections, you explored the average gradient and the average rate of change — both measured over an interval. Now we take a crucial step: what…
- [Uses of the Derivative](https://www.hlayiso.com/grade-12/mathematics/notes/differential-calculus/uses-of-the-derivative) — Uses of the Derivative Now that you can find the derivative of a function, it is time to see what you can do with it. The derivative has three major applications in Grade 12: finding the equation of…
- [Drawing the Graph of a Cubic Polynomial](https://www.hlayiso.com/grade-12/mathematics/notes/differential-calculus/drawing-the-graph-of-a-cubic-polynomial) — Drawing the Graph of a Cubic Polynomial The cubic function is one of the most important functions you will encounter in Grade 12 Differential Calculus. In this section, you will learn how to use the…

## Other Mathematics topics

- [Exponents and Surds](https://www.hlayiso.com/grade-12/mathematics/notes/exponents-and-surds)
- [Algebraic expressions, equations and inequalities](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities)
- [Number patterns](https://www.hlayiso.com/grade-12/mathematics/notes/number-patterns)
- [Functions and graphs](https://www.hlayiso.com/grade-12/mathematics/notes/functions-and-graphs)
- [Trig Functions](https://www.hlayiso.com/grade-12/mathematics/notes/trig-functions)
- [Finance, growth and decay](https://www.hlayiso.com/grade-12/mathematics/notes/finance-growth-and-decay)
- [Counting principle and probability](https://www.hlayiso.com/grade-12/mathematics/notes/counting-principle-and-probability)
- [Analytical Geometry](https://www.hlayiso.com/grade-12/mathematics/notes/analytical-geometry)
- [Trigonometry](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry)
- [Trigonometry: Sine, Cosine and Area Rules](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry-sine-cosine-and-area-rules)
- [Euclidean Geometry](https://www.hlayiso.com/grade-12/mathematics/notes/euclidean-geometry)
- [Statistics](https://www.hlayiso.com/grade-12/mathematics/notes/statistics)

## Frequently asked questions

### What is covered in Differential Calculus for Grade 12 Mathematics?

The Differential Calculus section covers all key concepts from the Grade 12 Mathematics CAPS curriculum, including detailed explanations, worked examples, and exam preparation tips.

### Are the Differential Calculus notes free?

Yes. Each section has a free preview, and a free Hlayiso account lets you read the full notes.

### How do these notes help with exam preparation?

Our Differential Calculus notes are CAPS-aligned and include worked examples, common mistakes to avoid, and exam tips — everything you need to prepare for your Grade 12 Mathematics exams.

### Are there quizzes for Differential Calculus?

Yes. Hlayiso has quizzes for Differential Calculus in Grade 12 Mathematics. Test your understanding after reading the notes.

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