# 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.

### Notes

These notes from MathCentre introduce the idea of the derivative (called the gradient function in the notes) and some associated notation and terminology. There are some short examples at the end for you to use for practice.

A pdf of this document can be downloaded here.

### 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.

### Notes

These notes from MathCentre explain the geometric idea behind differentiation from first principles and include some examples of how derivatives are calculated using this method.

A pdf of this document can be downloaded here.

### 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.