01 Calculus First Principles and Rules of Differentiation

Grade 12 Mathematics | Calculus: Differentiation from First Principles & Rules of Differentiation In this tutorial, we explore one of the most important concepts in Grade 12 Calculus: **Differentiation**. We begin by determining the derivative of a function using **First Principles**, helping learners understand where the rules of differentiation come from before applying them to more complex functions. Questions covered in this lesson: 1. Determine (f'(x)) from first principles if: [ f(x)=4x-7 ] 2. Determine (g'(x)) if: [ g(x)=2x^3-5x+6 ] 3. Determine (\frac{dy}{dx}) if: [ y=\frac{3x^2-4x+1}{x} ] What you will learn: ✔ Understanding the concept of a derivative ✔ Differentiation from first principles ✔ Applying the power rule for differentiation ✔ Simplifying algebraic expressions before differentiating ✔ Finding gradients of functions at any point ✔ Building a strong foundation for Grade 12 Calculus examinations This lesson is ideal for *CAPS, IEB, and Cambridge Mathematics learners* preparing for tests, examinations, and revision. Visit *Smartheducation* for more Mathematics resources, study guides, intervention programmes, and examination preparation courses: [www.smarth.education](http://www.smarth.education) If you found this tutorial helpful, remember to: • Like the video • Subscribe to the channel • Share with fellow learners • Turn on notifications for more Mathematics tutorials #Grade12Mathematics #Calculus #Differentiation #FirstPrinciples #Derivative #MathsTutorial #Smartheducation #CAPSMathematics #IEBMathematics #MatricMaths #LearnMaths