How to Differentiate Using First Principles (Formula and Examples)

Differentiation from First Principles | WASSCE Elective Mathematics Why do we say the derivative of x^2 is 2x? Before we learn all the "quick rules," we have to understand where they come from! In this video, we are diving deep into Differentiation from First Principles.The First Principle is the heart of Calculus. It’s the method of finding the gradient of a curve using the definition of a limit. While the shortcuts are great for objectives, examiners love to ask for the "First Principles" method in the theory section to see if you truly understand the math. ✏️ What we will cover :The Concept: Understanding the "Gradient at a point" the logic. The Formula: Breaking down so it actually makes sense.Step-by-Step Examples: Differentiating linear, quadratic, and simple rational functions from scratch. How to lay out your workings clearly to get full marks in your WASSCE or school exams. Don't let the algebra scare you—we’ll go slow and simplify every step. By the end of this video, you'll be able to derive a derivative for any basic function! Stay Connected:👍 Like the video if this cleared up the "First Principles" formula for you!🔔 Subscribe to join our study group as we move into the Power Rule next.💬 Comment below: Which function do you find the hardest to differentiate from first principles?🏷️ WASSCE Elective Maths, WAEC Elective Mathematics, Ghana SHS Maths, Nigeria SHS Maths, WASSCE 2026, Elective Maths Theory, SHS Calculus, West African Examinations CouncilTopic Specific:First principles of derivative, differentiation from first principles, definition of derivative, calculus basics, f(x+h) formula, limits and derivatives, elective maths differentiation, how to differentiate, math tutorial Africa