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In other words, how do you differentiate a piecewise function?

Are they just done in several parts, as if differentiating more than one function, and so then the derivative is also a piecewise function? I imagine then that if the seperate functions that make up the 'pieces' of the piecewise derivative are the same, then the derivative can then be rewritten as a non-piecewise function.

Is that the general idea?

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    Not only the general idea, but the exact idea! (Though I guess you have to be a *teeny* bit careful about differentiability at the endpoints when gluing together to make your non-piecewise derivative.)2012-01-06
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    That's the kind of response I like. Thanks! Maybe you can take a look at my follow up question http://math.stackexchange.com/questions/96990/question-about-finding-the-limit-at-an-undefined-point2012-01-06

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