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Math Help - deriv. of ln

  1. #1
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    deriv. of ln

    The question is find derivative of
    f(x) = sin(2ln x)

    So far, I've worked it out till here:

    cos(2lnx)(2/x+lnx)

    Is that correct? If so, how can I simplify it more?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by kwivo View Post
    The question is find derivative of
    f(x) = sin(2ln x)

    So far, I've worked it out till here:

    cos(2lnx)(2/x+lnx)

    Is that correct? If so, how can I simplify it more?
    no. the derivative of lnx is just 1/x
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  3. #3
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    I'm sorry. Math is not my best subject. So if I ask some pretty simple questions, excuse me.

    Ok, so is the cos(2lnx) part right? And for the inside function 2lnx, I didn't really know what to do with the 2 there. I know that the derivative of lnx is 1/x, but since the 2 was there, I used the product rule...which I guess is wrong?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by kwivo View Post
    I'm sorry. Math is not my best subject. So if I ask some pretty simple questions, excuse me.

    Ok, so is the cos(2lnx) part right? And for the inside function 2lnx, I didn't really know what to do with the 2 there. I know that the derivative of lnx is 1/x, but since the 2 was there, I used the product rule...which I guess is wrong?
    you don't use the product rule when you have a constant in front, the constant just stays there. and even if you did use the product rule, the derivative of a constant is zero, so it would wipe out the extra part. the derivative of 2ln(x) is simply 2/x
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  5. #5
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    Ok, thanks for the clarification. So, it is cos(2lnx)(2/x). Is there a way to simplify more?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by kwivo View Post
    Ok, thanks for the clarification. So, it is cos(2lnx)(2/x). Is there a way to simplify more?
    no, not really. i'd probably write 2cos(2lnx)/x
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  7. #7
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    Quote Originally Posted by Jhevon View Post
    no, not really. i'd probably write 2cos(2lnx)/x
    I would hope you would write:

    2 cos(2 ln(x)) / x

    I hate function arguments just placed next to the function name, its sloppy. Also extra speces make things easier to read!

    RonL
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