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Math Help - Chain rule question-Is this correct?

  1. #1
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    Chain rule question-Is this correct?

    Could someone please double check my workings.

    I have this equation
    Y=[4th root(x^2+4)]^3

    Rearranged is [(x^2+4)^1/4]^3

    When I apply the chain rule…
    Y=[(x^2+4)^1/4]^3

    U=(x^2+4)^1/4…..
    u`=1/4(x^2+4)^-3/4.2x

    Y=u^3…..
    Y`=3u^2

    =u`.y`……3[1/4(x^2+4)^-3/4.2x]^2
    =……….. 3[1/2x(x^2+4)^-3/4]^2
    =………... [3/2x(x^2+4)^-3/4]^2
    =…………3x/2(x^2+4)^(-3/4+2/4)]
    =…………3x/2(x^2+4)^-1/4

    Solution is ……3x/[2(x^2+4)^1/4]

    Is my workings correct?
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  2. #2
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    Quote Originally Posted by Neverquit View Post
    Could someone please double check my workings.

    I have this equation
    Y=[4th root(x^2+4)]^3

    Rearranged is [(x^2+4)^1/4]^3

    When I apply the chain rule…
    Y=[(x^2+4)^1/4]^3

    U=(x^2+4)^1/4…..
    u`=1/4(x^2+4)^-3/4.2x

    Y=u^3…..
    Y`=3u^2

    =u`.y`……3[1/4(x^2+4)^-3/4.2x]^2
    =……….. 3[1/2x(x^2+4)^-3/4]^2
    =………... [3/2x(x^2+4)^-3/4]^2
    =…………3x/2(x^2+4)^(-3/4+2/4)]
    =…………3x/2(x^2+4)^-1/4

    Solution is ……3x/[2(x^2+4)^1/4]

    Is my workings correct?
    Dear Neverquit,

    Your final answer, \frac{3x}{2(x^2+4)^{\frac{1}{4}}} is correct.
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