Derivative of x² from First Principles | Step-by-Step Calculus

In this lesson, we break down the First Principles of Differentiation step by step and apply it to find the derivative of y = x². This is a foundational concept in calculus – understanding where derivatives come from before moving on to shortcut rules. 📌 What you'll learn: The limit definition of the derivative How to set up the difference quotient Step-by-step algebraic simplification for x² The final derivative: dy/dx = 2x ✅ Why first principles matter: They show the true meaning of a derivative as an instantaneous rate of change, building intuition for all of calculus. 🎯 Perfect for: Calculus beginners Students preparing for exams (IB, A-Level, AP Calculus, university foundation) Anyone who wants to understand why differentiation works, not just how 📘 Next videos in this series: First Principles: y = √x First Principles: y = 1/x First Principles: y = constant 🔔 Like, subscribe, and hit the bell for more step-by-step calculus tutorials. #Calculus #FirstPrinciples #Derivative #MathTutorial #Differentiation