@seleniumed: Before you ever memorise a differentiation rule, there is a deeper question: where do those rules actually come from? The answer is differentiation from first principles - the definition of the derivative itself. The idea is beautifully simple. To find the gradient of a curve at a single point, you start by drawing a straight line between two points on the curve. The gradient of that line is just rise over run - the change in y divided by the change in x. Mathematically, that is (f(x + h) minus f(x)) divided by h, where h is the horizontal gap between the two points. Now here is the key move: you shrink h towards zero. As h gets smaller and smaller, the two points get closer together, and the straight line tilts until it becomes a tangent - touching the curve at exactly one point. The gradient of that tangent is the derivative. This limiting process is written as the limit as h approaches zero of (f(x + h) minus f(x)) divided by h. It is not just a formula - it is the precise definition of what a derivative means. Apply it to f(x) = x squared and you get 2x. That is the power rule, derived from scratch with no shortcuts. Every differentiation rule you have ever used - product rule, chain rule, quotient rule - ultimately traces back to this single limit. Follow @seleniumed for more physics and math explained visually. #tiktok #viral #mathematics #calculus #derivatives

Selenium

Open In TikTok:

Region: AU

Saturday 04 July 2026 02:03:00 GMT