# HL AA – Differentiation

## First Principles

## sin, cos, ln, e

## Inflexion Points

## L'Hopitals

## Tangents/Normals

## Product/Quotient

## Optimisation

## Implicit differentiation

## Chain Rule

## Maximum/Minimum

## Higher Orders

## Differentiation Review

## Traffic Light Coding for Unit

Make your own copy and share with your students.

##### Learning Outcomes

Understand the concept of a limit from a table or graph. |

Understand that the derivative is a gradient or rate of change function, and its notation. |

Understand when functions are increasing or decreasing. |

Simple derivatives by reducing the powers, e.g axn |

Find the equations of tangents and normals to functions. |

Derivatives of sinx, cosx, lnx, and ex. |

Use and understand the chain rule. |

Use and understand the product and quotient rules. |

Understand the concept of maximum and minimum points. |

Find the second derivative, and use this distinguishing between maximum and minimum points |

Finding points of inflexion. |

Using differentiation for solving optimization problems. |

Understand informally continuity and differentiability of a function at a point. |

Differentiate from first principles using the concept of a limit. |

Use differentiation for higher orders (greater than the second derivative). |

Evaluation of a limit using Maclaurin’s Series or l’Hopital’s rule, and the repeated use of l’Hopital’s rule. |

Use implicit differentiation for related rates of change and optimization problems. |