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Math Help - chain rule

  1. #1
    Senior Member euclid2's Avatar
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    chain rule

    Can someone explain with a simple example what the chain rule is and how to use it?
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  2. #2
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    Put simply......

    Chain rule - Wikipedia, the free encyclopedia

    Wikipedia explains it about as laymans as it can be.

    Regards
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  3. #3
    Eater of Worlds
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    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 \sqrt{x^{2}+2x}=(x^{2}+2x)^{\frac{1}{2}}

    Take the derivative of the outside:

    \frac{1}{2}(x^{2}+2x)^{\frac{-1}{2}}

    Take the derivative of the inside: \frac{d}{dx}[x^{2}+2x]=2x+2

    Now, multiply them:

    \frac{1}{2}(x^{2}+2x)^{\frac{-1}{2}}\cdot (2x+2)

    Simplify and make it 'purdy':

    \frac{x+1}{\sqrt{x^{2}+2x}}

    See there?. Now you try it with, say, sin(x^{3}) and show me what you get.
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  4. #4
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    nice (and simple) presentation of the chain rule.

    The Chain Rule
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  5. #5
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    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
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