Learn: Differentiation Basics

Welcome!Today we’ll explore differentiation, a key topic in calculus. This lesson is personalised to help you master the basics of differentiation step by step!

What is Differentiation?Differentiation is a mathematical process used to find the rate at which one quantity changes with respect to another. It helps us calculate the slope of a curve at any given point, which is especially useful for analysing graphs or solving problems involving rates of change.

Basic Rules of DifferentiationThe process of differentiation uses certain rules to find derivatives (the results of differentiation). Here are the key rules:Power Rule: If f(x) = x^n, then f'(x) = n*x^(n-1).Constant Rule: The derivative of a constant is always 0.Sum Rule: The derivative of a sum is the sum of the derivatives.

Why Differentiation MattersUsing differentiation, we can solve problems involving rates of change, such as velocity in physics or growth rates in economics. It’s also helpful for finding turning points on graphs to analyse maximum or minimum values.

Applying DifferentiationLet’s practise applying the rules. For example, if f(x) = 4x^2 + 3x + 2, differentiate each term separately. The derivative is 8x + 3 because the constant rule applies to 2, and the power rule applies to 4x^2 and 3x.

Review Time!Great work! You’ve learned about differentiation, key rules, and how to apply them. Let’s test your understanding with some final questions.