**General Relativity For
Tellytubbys**

**Miscellaneous Mathematics**

**Sir Kevin Aylward B.Sc., Warden of the Kings
Ale**

**Back to the Contents section**

This section is a refresher to bits of stuff that, if you don't already know, you had better resign yourself to flipping hamburgers for one or two years yet, before you have any hope of inventing a new Warp Drive. Not all of the details will be filled in cos I can not be bothered.

__Derivative Chain Rule__

Consider a function that is a function of a function i.e.

Forming the derivative of this gives

Now suppose that the function is a function of more then one function

With a bit of piddling about, using the standard derivative of product rules, the partial derivative can be found to be

Or in more general terms, for an arbitrary number of functions, F can be written as:

then

__ __

__ __

This can be written more compactly as:

Where it is now assumed that repeated index's in a product will be summed, even though no sigma sign is shown.

Finally, if F is a set of function of set of variables x, y, z, one can generally write

or

Then, it can be written

© Kevin Aylward 2000 - 2015

All rights reserved

The information on the page may be reproduced

providing that this source is acknowledged.

Website last modified 31^{st} May
2015

http://www.kevinaylward.co.uk/gr/index.html