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Math Help - Derivative of a composite function

  1. #1
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    Derivative of a composite function

    Hi, I have a test tomorrow and have been trying to do this review question, but I keep getting the wrong answer:

    If y = 5u^2 + 3u -1 and u = 18/(x^2 + 5), find dy/dx when x =2.

    I found y', then found u'. I subbed x = 2 into u' to get -72/81. Then I subbed 2 into the original u equation, and found u = 2. I subbed that into y' to get 23. 23 X (8/9) for the final answer, but this is wrong. I'm not sure if I made a mistake with derivatives or what, but I'd reallyyy appreciate any help. Thank you!
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  2. #2
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    Show your solution.

    This way is easy to check where the mistake is.
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  3. #3
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    y' = 10u + 3

    u' = -(2x)(18) / (x^2+5)^2

    = -36x/(x^2 + 5)^2


    u' (2) = -36(2)/(4+5)^2
    = -72/81 --> -8/9

    Then u = 18/(2^2) + 5 = 2

    So y'(2) = 10(2) + 3 = 23


    23 x -8/9 = -184/9
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by starswept View Post
    y' = 10u + 3

    u' = -(2x)(18) / (x^2+5)^2

    = -36x/(x^2 + 5)^2


    u' (2) = -36(2)/(4+5)^2
    = -72/81 --> -8/9

    Then u = 18/(2^2) + 5 = 2

    So y'(2) = 10(2) + 3 = 23


    23 x -8/9 = -184/9
    your mistake is at the first step. you have to differentiate implicitly (with respect to x)

    y = 5u^2 + 3u - 1

    => y' = 10u*u' + 3u'
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