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Math Help - Derivatives of Logarithmic Functions -Fractions-

  1. #1
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    Derivatives of Logarithmic Functions -Fractions-

    Hello everyone.

    I got a question regarding the derivatives of a log but in a fraction. Here is an example:

    3x^2 / ln(x)

    This isnt a homework problem but im studying for a quiz tomorrow and want to be ready for anything. Would I use the quotient rule for this problem?



    Also another quick question. Its kind of stupid so sorry.
    But in this question how do i get from step 1 to step 2.

    x= 1
    y = sin (7 ln(x))
    (derivative) dx/dy y= cos(7ln(x)) (7/x)


    Step 1: y(1) = cos (7ln(1)) (7/1)
    Step 2: y(1) = cos (0) (7)

    Im guessing ln (1) = 0 ?


    thanks for your help
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  2. #2
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    Quote Originally Posted by GirouxCalder View Post
    Hello everyone.

    I got a question regarding the derivatives of a log but in a fraction. Here is an example:

    3x^2 / ln(x)

    This isnt a homework problem but im studying for a quiz tomorrow and want to be ready for anything. Would I use the quotient rule for this problem?
    Hi GirouxCalder,

    Yes for this you would use the quotient rule. Just take note that \frac{d}{dx} \ln(x) = \frac{1}{x}. So you'll end up with a fraction in your larger fraction, which just means a little tricky simplification. I think these problems are missed more on the algebra used to clean up the answer than the actual derivative.

    Jameson
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  3. #3
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    Quote Originally Posted by GirouxCalder View Post
    Also another quick question. Its kind of stupid so sorry.
    But in this question how do i get from step 1 to step 2.

    x= 1
    y = sin (7 ln(x))
    (derivative) dx/dy y= cos(7ln(x)) (7/x)


    Step 1: y(1) = cos (7ln(1)) (7/1)
    Step 2: y(1) = cos (0) (7)

    Im guessing ln (1) = 0 ?
    Yes ln(1)=0.

    Remember that if \ln(a)=b, this is equivalent to saying e^b=a. Here a=1, so b must be zero for this statement to be true.
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    Thanks, I still just cant figure these problems out though... I think if i can get one i will be able to get the rest. Mind helping me?

    heres a example:

    4 / (ln(x))^2

    for some reason i get the concept but cant understand how to solve it....
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  5. #5
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    Quote Originally Posted by GirouxCalder View Post
    Thanks, I still just cant figure these problems out though... I think if i can get one i will be able to get the rest. Mind helping me?

    heres a example:

    4 / (ln(x))^2

    for some reason i get the concept but cant understand how to solve it....
    Well this one can be done just as easily using the power and chain-rule, or by the quotient rule. Since you asked about the quotient rule, I'll do it that way.

    \frac{d}{dx} \frac{4}{(\ln x)^2} = \frac{[(\ln x)^2 *0] -(4)[2(\ln(x))*(\frac{1}{x})]}{(\ln x)^4}

    Simplifying,

    ... = - \frac{8}{x(\ln x)^3}
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