Learn: Differentiation

Welcome!Today we will explore differentiation, a key concept in calculus that helps us understand rates of change. This is an exciting topic with many real-world applications. Let’s get started!

What is Differentiation?Differentiation is the process of finding the derivative of a function. A derivative tells us the rate at which one quantity changes with respect to another. It’s used to find slopes of curves, rates of change, and optimise problems in maths and real life.

The DerivativeThe derivative of a function measures how the function changes as its input changes. For example, if you have a graph of distance against time, the derivative represents speed, which is how fast the distance is changing.

Basic Rules of DifferentiationThere are key rules for differentiation that make it easier to find derivatives. For example, the power rule states: if f(x) = xn, then f'(x) = n × xn-1. Another rule is the constant rule: the derivative of a constant is 0.

Applications of DifferentiationWe use differentiation to solve problems like finding the maximum profit, minimum cost, or the slope of a hill. For example, if you’re designing a ramp, you can use differentiation to calculate the steepness at any point.

Review Time!Great work! You've learned about differentiation, derivatives, and their applications. Now let’s test your understanding with a few questions.