Can someone explain with a simple example what the chain rule is and how to use it?

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- Jan 4th 2009, 02:39 PMeuclid2chain rule
Can someone explain with a simple example what the chain rule is and how to use it?

- Jan 4th 2009, 02:46 PMRossBrons
Put simply......

Chain rule - Wikipedia, the free encyclopedia

Wikipedia explains it about as laymans as it can be.

Regards - Jan 4th 2009, 02:51 PMgalactus
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. - Jan 4th 2009, 02:52 PMskeeter
nice (and simple) presentation of the chain rule.

The Chain Rule - Jan 4th 2009, 02:54 PMSimplicity
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