# Introduction to Differentiation

## The Idea of Differentiation

## Video

These videos from the *UCD Maths Support Centre* give a geometric explanation of the idea behind differentiation.

Note: All *UCD Maths Support Centre* content is available for free at www.youtube.com/channel/UCLjiq31tqpoHNqt9M43sqZw.

UCD Math Support Centre’s Website: www.ucd.ie/msc.

Note: All *UCD Maths Support Centre* content is available for free at www.youtube.com/channel/UCLjiq31tqpoHNqt9M43sqZw.

UCD Math Support Centre’s Website: www.ucd.ie/msc.

## The Derivative

## Video

This video from *Firefly Lectures* explains the idea of differentiability at a point and goes through a couple of examples.

Note: All *Firefly Lectures* content is available for free at www.fireflylectures.com.

This video from *Khan Academy* works through an example of analysing a function for both continuity and differentiability. In this case the function is continuous but not differentiable at a certain point.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

## Differentiation from First Principles

## Videos

This video from the *UCD Maths Support Centre* shows how to compute the derivative of a quadratic function using first principles.

Note: All *UCD Maths Support Centre* content is available for free at www.youtube.com/channel/UCLjiq31tqpoHNqt9M43sqZw.

UCD Math Support Centre’s Website: www.ucd.ie/msc.

## Derivatives of Standard Functions

## Notes

These notes from MathCentre give a list of the standard functions that you will encounter in calculus, along with their derivatives.

A pdf of this document can be downloaded here.

## Interactive Exercises

You can practise differentiating some standard functions using this NUMBAS exercise.

Please click here to view this NUMBAS question in another window.

## Higher-Order Derivatives

## Video

This video from *MySecretMathTutor* shows how to compute higher-order derivatives for various functions and includes a product rule example at the end.

Note: All *MySecretMathTutor* content is available for free at www.youtube.com/user/MySecretMathTutor.

MySecretMathTutor‘s Website:www.mysecretmathtutor.

These notes from HELM of Loughborough University introduce higher-order derivatives, their notation, and how to compute them.

A pdf of this document can be downloaded here.