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Math Help - Simplify derivative

  1. #1
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    Simplify derivative

    Can someone please show me how this derivative: f'(x) = x^3(18x) - (9)(x^2 - 3)(3x^2)/(x^3)^2

    Simplifies to this: 9(9 - x^2)/ x^4

    Because I am lost lol

    Here is the original equation:
    f(x)= 9(x^2-3)/x^3

    Thanks
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  2. #2
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    Quote Originally Posted by Jwd41190 View Post
    Can someone please show me how this derivative: f'(x) = x^3(18x) - (9)(x^2 - 3)(3x^2)/(x^3)^2

    Simplifies to this: 9(9 - x^2)/ x^4

    Because I am lost lol

    Here is the original equation: f(x)= 9(x^2-3)/x^3

    Thanks
    It's really easier if you expand

     <br />
f(x) = \frac{9x^2}{x^3} - \frac{27}{x^3} = \frac{9}{x} - \frac{27}{x^3}<br />
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  3. #3
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    Thats still not right is it here it is from the book

    Here it is from the book:
    http://img121.imageshack.us/img121/3689/scn0001.jpg
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  4. #4
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    Quote Originally Posted by Danny View Post
    It's really easier if you expand

     <br />
f(x) = \frac{9x^2}{x^3} - \frac{27}{x^3} = \frac{9}{x} - \frac{27}{x^3}<br />
    What I'm saying is I think that this way is the easiest. However, if you use th equotient rule then

     <br />
\frac{x^3 (18x) - 9(x^2-3)(3x^2)}{x^6} = \frac{18x^4 - 27x^4+81x^2}{x^6} = \frac{ - 9x^4+81x^2}{x^6} =\frac{ - 9x^2+81}{x^4}  =\frac{ 9(9 - x^2)}{x^4}
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