Topic 3: Introduction to differential calculus — Maths Interactives

Rates of change and the concept of derivatives

10 hours

Determine average rate of change in a variety of practical contexts. 1 interactive
Use the rule 𝑓′(𝑥) = lim ℎ→0 𝑓(𝑥+ℎ)−𝑓(𝑥) ℎ to determine the derivative of simple power functions and polynomial functions from first principles. 1 interactive
Interpret the derivative as the instantaneous rate of change.
Interpret the derivative as the gradient of a tangent line of the graph of 𝑦 = 𝑓(𝑥). 1 interactive
Use the rule 𝑑 𝑑𝑥𝑥𝑛 = 𝑛𝑥𝑛−1 for positive integers.
Understand the concept of the derivative as a function. 1 interactive
Recognise and use properties of the derivative 𝑑 𝑑𝑥 (𝑓(𝑥) + 𝑔(𝑥)) = 𝑑 𝑑𝑥𝑓(𝑥)+ 𝑑 𝑑𝑥𝑔(𝑥).
Calculate derivatives of power and polynomial functions.