Differentiation

Introduction to Differentiation

• Understand the concept of a derivative of a function, which represents the slope or rate of change of the function at a given point.
• Familiarise yourself with the notation of differentiation, such as f’(x) or df/dx.
• Appreciate the geometrical interpretation of the derivative: it is the gradient of the tangent to the curve at a point.
• Know how to find the derivative of a constant function and the power rule for the derivative of x^n.

Differentiation Rules

• Grasp the sum and difference rules, which allow you to take derivatives of functions that are made by adding or subtracting other functions.
• Learn the product and quotient rules, which are used when differentiating products and quotients of functions.
• Understand the chain rule for the derivative of a composite function.
• Recognise the derivatives of trigonometric, exponential and logarithmic functions and know how to apply these to solve problems.

Applications of Differentiation

• Understand how to use differentiation to find stationary points (maxima, minima and points of inflection) of a function.
• Be able to apply differentiation to solve problems involving rates of change, such as velocity and acceleration in kinematics.
• Know how to use the second derivative test to determine the nature of the stationary points.
• Use differentiation to find the equation of a tangent or normal to a curve at a given point.

Implicit Differentiation

• Develop an understanding of implicit differentiation and its role when equations are not explicitly solved for y.
• Learn techniques to differentiate implicitly defined functions.
• Practice applying implicit differentiation in problems where explicit differentiation is not applicable.

Remember, this content is intended to assist your revision process and should be used in conjunction with classroom materials, textbooks, and other resources. Plenty of practise is key for mastering the concept of differentiation.