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Thread: Differentiating a fraction

  1. #1
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    Question Differentiating a fraction

    ok i have this question and need some urgent help, i have to hand this in tomorrow and im rapidly falling very tired;

    i am studying AS level mathematics on the aqa syllabus...


    i have this question for homework:

    A curve has the equation: $\displaystyle Y= X^4/4 + 32/X^2$

    A: find $\displaystyle dy/dx$

    i dont simply want the answer is it possible for anyone to give me a worked solution?


    thnx in advance: Smithswood
    Last edited by Smithswood; Jan 23rd 2008 at 11:50 AM.
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  2. #2
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    Quote Originally Posted by Smithswood View Post
    ok i have this question and need some urgent help, i have to hand this in tomorrow and im rapidly falling very tired;

    i am studying AS level mathematics on the aqa syllabus...


    i have this question for homework:

    A curve has the equation: Y= X^4/4 + 32/X^2

    A: find dy/dx

    i dont simply want the answer is it possible for anyone to give me a worked solution?


    thnx in advance: Smithswood
    $\displaystyle y = \frac{x^4}{4} + \frac{32}{x^2} = \frac{x^4}{4} + 32 x^{-2}$.

    Now apply the well known rule (to each term) that the derivative of $\displaystyle a x^n$ is $\displaystyle n a x^{n-1}$.
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  3. #3
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    so...?

    so$\displaystyle \frac{x^4}{4}$

    would become $\displaystyle 4x^3$

    and how did you get $\displaystyle 32x^-2$?
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  4. #4
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    Quote Originally Posted by Smithswood View Post
    so$\displaystyle \frac{x^4}{4}$
    would become $\displaystyle 4x^3$
    No it would become $\displaystyle \frac{4x^3}{4}=x^3$



    Quote Originally Posted by Smithswood View Post
    and how did you get $\displaystyle 32x^-2$?
    $\displaystyle \frac{a}{b^n}=ab^{-n}$
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  5. #5
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    therefore...

    would it not be $\displaystyle 32x^-1$

    as $\displaystyle 32 = 32x^1$?

    $\displaystyle 1 - 2 = -1$???
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  6. #6
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    Quote Originally Posted by Smithswood View Post
    would it not be $\displaystyle 32x^-1$
    No $\displaystyle \frac{32}{x^2}=32x^{-2}$ Note, this has not been differentiated yet.
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