Can someone explain with a simple example what the chain rule is and how to use it?
Put simply......
Chain rule - Wikipedia, the free encyclopedia
Wikipedia explains it about as laymans as it can be.
Regards
Without using the 'official' notation, the chain rule is essentially the derivative of the inside times the derivative of the outside. That is a simplistic definition, but here is an example.
We want the derivative of $\displaystyle \sqrt{x^{2}+2x}=(x^{2}+2x)^{\frac{1}{2}}$
Take the derivative of the outside:
$\displaystyle \frac{1}{2}(x^{2}+2x)^{\frac{-1}{2}}$
Take the derivative of the inside: $\displaystyle \frac{d}{dx}[x^{2}+2x]=2x+2$
Now, multiply them:
$\displaystyle \frac{1}{2}(x^{2}+2x)^{\frac{-1}{2}}\cdot (2x+2)$
Simplify and make it 'purdy':
$\displaystyle \frac{x+1}{\sqrt{x^{2}+2x}}$
See there?. Now you try it with, say, $\displaystyle sin(x^{3})$ and show me what you get.
nice (and simple) presentation of the chain rule.
The Chain Rule
Math Centre (www.mathcentre.ac.uk) explains it in a clear manner too, includes examples and problems to try out. See their Chain Rule Booklet: http://www.mathcentre.ac.uk/resource...-chain-feb.pdf