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Math Help - Are these the correct derivatives for these functions?

  1. #1
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    Are these the correct derivatives for these functions?

    use the quotient rule to differentiate the function

    k(x)= (e^6x)/(x^3+8)

    I have got as far as

    k '(x) =(x^3+8)(6e^6x)-(e^6x)(3x^2)/(x^3+8)^2

    But im unsure how to take it any further would anyone be able to help us?
    Last edited by Orlando; March 8th 2012 at 05:54 AM.
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  2. #2
    MHF Contributor Siron's Avatar
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    re: Are these the correct derivatives for these functions?

    Your answer is correct! The only thing you can do is put a factor 3e^{6x} outside in the numerator.
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  3. #3
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    re: Are these the correct derivatives for these functions?

    so would that make it

    k'(x)= e^6x(6x^3+48-3x^2)/(x^3+8)^2
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  4. #4
    Senior Member x3bnm's Avatar
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    re: Are these the correct derivatives for these functions?

    Quote Originally Posted by Orlando View Post
    so would that make it

    k'(x)= e^6x(6x^3+48-3x^2)/(x^3+8)^2
    What Siron meant is this:

    \frac{dk}{dx} = \frac{3e^{6x}(2x^{3} + 16 - x^{2})}{(x^{3} + 8)^{2}}

    You just factor 3e^{6x} using simple algebra.

    You can also find differentiation of k(x)= \frac{e^{6x}}{x^3+8} in the following link:

    differentiate (e^(6x))/(x^3+8) - Wolfram|Alpha
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