Differentiation
Differential calculus is the area of mathematics concerned with describing and analysing change. It provides tools for measuring how one quantity varies in response to another, allowing us to explore rates of change, growth and decay, and how functions behave locally. It focuses on calculating the derivative, a measure of how a function is changing at any given point. The derivative gives the slope of the tangent line to a curve, capturing its immediate direction and steepness.
Differential calculus underpins many real-world applications. It helps us understand motion by relating position, velocity and acceleration, allows us to model biological and chemical processes that grow or decay, supports optimisation in business, engineering and data science and it provides insight into how systems respond to changes in inputs or external conditions.
This resource revises differentiation and within differentiation there are 7 key concepts:
- Average rate of change
- Instantaneous rate of change
- Common derivatives and differentiation techniques
- Derivative graphs
- Stationary points
- Applications of differential calculus
To determine if this resource will benefit you, start by answering the following questions:
- How are the average rate of change and the instantaneous rate of change of a function related?
- How are the chain rule, product rule and quotient rule used to simplify differentiation?
- How can differential calculus by applied to real-world problems?