Differentiation

Understanding Differentiation

• Gain a deep understanding of the concept of differentiation and the process of finding the derivative of a function.
• Explore the central idea of the rate of change and how it is represented by the derivative.
• Understand what it means for a function to be differentiable and recognise the conditions where a function may not be differentiable.

Techniques of Differentiation

• Master the various techniques of differentiation including the product rule, quotient rule, and chain rule.
• Apply these rules to differentiate polynomial functions, exponential and logarithmic functions, as well as trigonometric functions.
• Recognise the importance of the constant rule and power rule and learn how to use the relevant differentiation tables efficiently.

Higher-Order Derivatives

• Differentiate a function more than once to identify second-order and higher-order derivatives.
• Understand the significance of these higher-order derivatives, such as the role of the second derivative in determining concavity of a function.

Applications of Differentiation

• Apply differentiation to solve problems that require determining rates, including those relating to velocity and acceleration.
• Learn the method of using derivatives to locate points of maximum and minimum (both absolute and relative), known as extrema, on the graph of a function.
• Recognise the role of differentiation in curve sketching and optimisation problems.
• Explore the relation of the derivative in understanding the concept of limit and establishing related proofs.

Implicit and Parametric Differentiation

• Explore the concepts of implicit differentiation and its uses in tackling complex functions.
• Understand the concept of parametric differentiation and how to find the derivative of a function given parametrically.
• Solve real-world problems involving these advanced differentiation techniques.