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Math Help - derivation of absolute value

  1. #1
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    derivation of absolute value

    Hi everyone

    I've a question involving derivation of absolute values, if you look at the attached picture you will see what I couldn't understand as shown in a rectangle. I couldn't get that part. It will be much appreciated if someone can explain how it happens


    thanks...
    Attached Thumbnails Attached Thumbnails derivation of absolute value-question-absolute.jpg  
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  2. #2
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    y = \sqrt{u^2}

    We use the chain rule to differentiate this. Differentiate the square root, then the inside part:

    (\sqrt{u^2})' = \frac{1}{2\sqrt{u^2}} \cdot 2u

    = \frac{\not{2}u}{\not{2}\sqrt{u^2}}

    = \frac{u}{\sqrt{u^2}}

    = \frac{u}{|u|}

    You have to know that, if n is even, then:
    \sqrt[n]{x^n} = |x|
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  3. #3
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    got it many thanks...
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