Calculus from First Principles

Simple Rules of differentiation

The Product Rule

Chain Rule

Derivatives of Trig, log and exponential functions

Tangents and Normals

Increasing and Decreasing functions

Points of inflection

Implicit differentiation

Optimisation

Introducing Derivatives

Chain Rule

Product and Quotient Rule

Tangents and Normals

Graphs and Derivatives

Differentiation Practice 1

Differentiation Practice 2

Differentiation Practice 3

Differentiation Practice 4

Inflection points, min/max

Normals Practice

MS

Optimisation 2 Practice

End of Year 1 Differentiation Topics

Markscheme

Investigation - River Crossing

Related Rates

Further Differentiation

Optimisation

Tangent line Practice

MS

Kognity 5.1 Limits and Gradients

Kognity 5.1 Gradients and Rates of Change

Kognity 5.2 - Graph Properties

Kognity 5.3 - Power and Constant Rules

Kognity 5.3 - Sum and Combination Rules

Kognity 5.4 - The Tangent Line

Kognity 5.4 - The Normal

Kognity 5.6 - Power Rule and Exponential Derivatives

Kognity 5.6 - Natural Logs and Trig derivatives

Kognity 5.6 - Chain Rule

Kognity 5.6 - Product and Quotient Rule

Kognity 5.7 - Increasing and decreasing behaviour

Kognity 5.7 - Second derivative

Kognity 5.7 - Convexity

Kognity 5.7 - Graphs and their derivatives

Kognity 5.8 Min and Max points

Kognity 5.8 - Optimisation

HL Kognity 5.12 Limits and convergence

HL Kognity 5.12 - Continuity

HL Kognity 5.12 - Differentiability

HL Kognity 5.12 - First Principles

HL Kognity 5.12 - Higher derivatives

HL 5.13 L'Hopital's Rule

HL 5.15 - Further Trig derivatives

HL 5.15 - Further expo/log derivatives

HL 5.15 Inverse Trig derivatives

HL 5.14 - Implicit differentiation

HL 5.14 - Related Rates of Change