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Math Help - Chain Rule

  1. #1
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    Chain Rule

    Reviewing the chain rule.

    1. 8sqrt(x^4-4x^2)

    I don't know if I'm simplifying it wrong, but I'm not getting the correct answer.

    2. csc^2x^2

    I don't know why these always give me a hard time. =/

    Any help would be greatly appreciated.

    Thanks!
    Last edited by alreadyinuse; November 27th 2007 at 08:38 PM.
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  2. #2
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    1. 8sqrt(x^4-4x^2)

    MATH]8*(x^4-4x^2)^(1/2)[[/tex]....exponentially sqrt=x^(1/2)

    Outer function is y= 8u^(1/2)
    Inner function is u=x^4- 4x^2
    rememberthe chain rule is dy/dx= dy/du * du/dx

    Derivativeof y= 8u^(1/2) ..... power rule


    8*.5u^(1/2-1)

    \frac{1}{8sqrt (u)}

    Now,
    \frac{1}{8sqrt (x^4- 4x^2)} * 4x^3 - 8x

    Then simplify,
    \frac{4x^3 - 8x}{8sqrt (x^4- 4x^2)}


    2. Use parenthesis to say what the equation is.
    Is it (csc^2x)^2 or perhaps (csc)^2x^2 ?
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  3. #3
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    The answer is (16x^2-32)/(sqrt (x^2-4)).

    I got (16x^2-32)/(sqrt (x^4-4x^2)).

    I have no idea where their answer came from.

    The second is written as (csc)^2(x^2)
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