Y1 Differentiation

• Differentiating polynomial expressions of the form ax^n

• Gradients: Using differentiation to solve problem including finding the gradient at a point

• Using differentiation to find the stationary points of a curve including use of the second differential to identify the nature of a turning point (max or min)

• Finding the equations of a tangents or a normal at a point on a curve

• Optimisation. This is using differentiation to solve practical problems

• Differentiation from first Principles

Differentiate from First Principles

1) Intro

2) Example

Differentiation Basics

1) Differentiate Polynomials

2) Fractional/Negative Indices

3) Handling Indices

Gradients and Turning Points

1) Introducing Turning points

2) Finding a Stationary point

3) Increasing/Decreasing functions

Tangents and Normals

1) Finding a Tangent

2) Finding a Normal

Optimisation (Practical Calculus)

Example 1

Example 2

Example 3

Example 4

Exam Question