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Math Help - 2nd and 3rd Derivatives!!!!!

  1. #1
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    2nd and 3rd Derivatives!!!!!

    Hi! This is my last question, I need the 2nd and 3rd derivatives of (lnx) / (8x). I have the first derivative as being (8-8lnx) / (64x^2) is that right?? I'm not sure!!! And I need the next 2 derivatives!!! THank you!!!
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  2. #2
    Junior Member bleesdan's Avatar
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    OK, your first one is right on.
    For the next two, just take the derivative of the derivative, then take the derivative of that!
    Remember, \frac{low*high'-high*low'}{low^{2}}
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  3. #3
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    Okay, for the second, I got (64x^2)(-8/x)-(8-8lnx)(128x) all over 4096x^4. Is that right?
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  4. #4
    Junior Member bleesdan's Avatar
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    Let's go back to the first derivative (I didn't see this the first time)
    Remember to reduce! You can pull an 8 out of there to get \frac{1-ln(x)}{8x^{2}}.
    Either way, your answer is technically right.
    I want you to simplify it, then post back with that.
    After that, you should go ahead and take another derivative.
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  5. #5
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    Oh okay, so if you take out a 8, then you're left with 1-lnx over 8x^2? So then finding the derivative of that, I got (-8x)-(1-lnx)(16x) all over 64x^4. Is that right?
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  6. #6
    Junior Member bleesdan's Avatar
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    Yep, but you still need to simplify this second derivative. What can you factor out of the top and the bottom?
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  7. #7
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    An 8? So I got (-x)-(1-lnx)(2x) all over 8x^4. No?
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  8. #8
    Junior Member bleesdan's Avatar
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    You're pretty close.
    You can get an x out too, so you get down to (-3+2ln(x)) over 8x^3
    With that, you can then take its derivative and get the third derivative
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  9. #9
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    Shouldn't it be all over 3x^4? How did you get 8x^3?
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  10. #10
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    I have to go to dinner now, but I will work on it!! THank you so much for helping me!!!!
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  11. #11
    Junior Member bleesdan's Avatar
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    Well, 8x^4 is 8x^3*x, so that's that.
    Have fun with supper! Glad to help, and tell your friends!
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  12. #12
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    Thanks!! I will tell my friends!!! I love this forum!!!! Buuuut my calc 2 ends tomorrow and I dont have to take another math class ever again. I will tell others though!!!!!! Thanks!!
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  13. #13
    Junior Member bleesdan's Avatar
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    What a shame.
    Well, go forth, then, into the realm of the world that doesn't make you take more math.
    Maybe I'll get there someday.
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  14. #14
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    hahaha okayyy!!
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