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Math Help - Inverse Derivatives!

  1. #1
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    Inverse Derivatives!

    Find the derivative of the function below.

    h(w) = w^3ln(6w)

    i keep coming up with the wrong answer...can someone tell me where im messing up

    my answer: 3(ln(6w))^2+w^2

    thanks

    mathlete
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  2. #2
    GAMMA Mathematics
    colby2152's Avatar
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    Quote Originally Posted by mathlete View Post
    Find the derivative of the function below.

    h(w) = w^3ln(6w)

    i keep coming up with the wrong answer...can someone tell me where im messing up

    my answer: 3(ln(6w))^2+w^2

    thanks

    mathlete
    First off, is the function this: h(w) = w^3ln(6w)

    or this? h(w) = w^{3ln(6w)}
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  3. #3
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    it's exactly what i wrote,

    h(w) = w^3(ln(6w))

    so its the first one you wrote down
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  4. #4
    GAMMA Mathematics
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    Quote Originally Posted by mathlete View Post
    it's exactly what i wrote,

    h(w) = w^3(ln(6w))

    so its the first one you wrote down
    In that case, you need to practice the product rule: h=fg; h'=f'g+fg'

    h(w) = w^3(ln(6w))

    h'(w) = 3w^2(ln(6w)) + \frac{6w^3}{6w}

    h'(w) = 3w^2(ln(6w)) + w^2

    It seems you either had a typo, or you misread something when applying the first term of the product rule.
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  5. #5
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    ahhh, yeah stupid mistake, i used the chain rule to get the derivative of
    ln(6w) which was more than i needed to do. Then i was still thinking chain rule and pluged in ln(6w) for w into 3w^2. thanks for the help...
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