
Learn what a derivative actually is — the exact steepness of a curve at a single point — and master the power rule, the fastest way to differentiate. You'll also learn to read the sign of a derivative to tell where a function is rising or falling.
The power rule alone can't handle functions that are nested, multiplied, or divided. This lesson adds three essential new tools — the chain rule, product rule, and quotient rule — so you can differentiate almost anything.
Put the derivative to work: find the equation of a tangent line that touches a curve at a point, and a normal line at right angles to it. A simple five-step method handles both.
Learn to read a function's entire shape from its derivative — where it rises, falls, and turns — then expand your toolkit with the derivatives of eˣ, ln x, and the trig functions.
This is where calculus solves real problems: finding the largest area, the lowest cost, the best possible value. Meet the second derivative and use it to tell a maximum from a minimum with confidence.
The final lesson ties everything together. See the derivative as a rate of change in real contexts like speed and growth, then learn related rates — using the chain rule to find how fast one quantity changes when it's linked to another.
This course contains the use of artificial intelligence.
This course is about calculus, starting with the very basics: Differentiation.
The name may sound intimidating at first, but this beginner friendly course will soon take you from the very first principles confidently solving real world problems.
We will first understand what a "derivative" really means, the way of measuring how fast something is changing, the slope a curve at any single point. From there, you will master essential techniques for differentiating complex functions, including power, chain, product and quotient rules, each taught through worked examples.
After building the base, you will soon enough be calculating tangents and normals of a curve, learning to read a function and spotting where it is increasing and decreasing. And finally, we will then work on optimisation - finding the maximum and minimum values to solve practical problems, and rate of change - which describes how quantities move around us in the real world.
Every idea is built up step by step and explained in simple language, which is then reinforced with examples and practice so it truly sticks. By the end, you will not just know the rules but build a deeper understanding bout what they mean, why they work, and their real world application.