Introduction to Differentiation

As the gateway to calculus, this topic introduces the study of rates of change by defining the derivative through both first principles and formal rules. Students learn to distinguish between average and instantaneous speed, exploring how the gradient of a curve at a single point can reveal where a function is increasing, decreasing, or stationary. By mastering the power rule and analyzing tangents and normals, students begin to use calculus to describe the motion and behavior of the physical world.