03 Calculus First Principles and Rules of Differentiation

Grade 12 Mathematics | Calculus: First Principles & Rules of Differentiation In this lesson, we explore key differentiation techniques used in Grade 12 Calculus. We begin by determining a derivative using *First Principles**, then apply the **Rules of Differentiation* to polynomial and rational functions. This tutorial provides clear, step-by-step solutions to help learners understand the concepts and develop confidence in solving examination-style questions. Questions covered in this tutorial: 1. Determine (f'(x)) from first principles if: [ f(x)=5-3x ] 2. Determine (g'(x)) if: [ g(x)=x^4-3x^2+2x-1 ] 3. Determine (\frac{dy}{dx}) if: [ y=\frac{x^2-5}{x^3} ] 📚 *What you will learn:* ✔ Differentiation from First Principles ✔ Understanding the derivative as the gradient of a function ✔ Applying the power rule correctly ✔ Differentiating polynomial functions ✔ Simplifying rational functions before differentiation ✔ Working with negative exponents ✔ Solving Grade 12 examination-style Calculus questions This tutorial is suitable for *CAPS, IEB, and Cambridge Mathematics learners* who are preparing for tests, assignments, examinations, and revision. 🌐 Visit *Smartheducation* for more Mathematics resources, intervention programmes, study guides, and examination preparation courses: [www.smarth.education](http://www.smarth.education) 👍 If you find this lesson helpful: • Like the video • Subscribe to the channel • Share with fellow learners • Turn on notifications for more Mathematics tutorials #Grade12Mathematics #Calculus #Differentiation #FirstPrinciples #Derivative #RulesOfDifferentiation #MatricMaths #CAPSMathematics #IEBMathematics #Smartheducation #LearnMaths