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Math Help - Need help with this derivative?

  1. #1
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    Need help with this derivative?

    The funciton is 3x/(x^2+4)
    I have no idea how to differentiate it. Step by step instructions would really help.
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  2. #2
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    Re: Need help with this derivative?

    Use the Quotient Rule.
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  3. #3
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    Re: Need help with this derivative?

    What's the quotient rule? I know the product rule is f(x)g'(x)+f'(x)g(x)
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    Re: Need help with this derivative?

    Quote Originally Posted by AFireInside View Post
    What's the quotient rule? I know the product rule is f(x)g'(x)+f'(x)g(x)
    If you don't know the Quotient Rule, you can use the Product Rule if you rewrite the function as 3x(x^2 + 4)^(-1)
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  5. #5
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    Re: Need help with this derivative?

    But what do i do with the -1 exponent?
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    Re: Need help with this derivative?

    Quote Originally Posted by AFireInside View Post
    But what do i do with the -1 exponent?
    You would need to use the chain rule to differentiate (x^2 + 4)^(-1)
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  7. #7
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    Re: Need help with this derivative?

    But then the -1 becomes a -2 and it doesn't really get you anywhere
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    Re: Need help with this derivative?

    Quote Originally Posted by AFireInside View Post
    But then the -1 becomes a -2 and it doesn't really get you anywhere
    What's wrong with that?
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  9. #9
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    Re: Need help with this derivative?

    Well using the chain rule (x^2+4)^-1 would become -(x^2+4)^-2 x (x^2+4).
    I don't see how that simplifies things.
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  10. #10
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    Re: Need help with this derivative?

    No it doesn't... It's the derivative of the inside times the derivative of the outside.
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  11. #11
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    Re: Need help with this derivative?

    Now I'm lost.
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  12. #12
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    Re: Need help with this derivative?

    The inside is u = x^2 + 4. What is its derivative?

    The outside is u^(-1). What is its derivative?
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    Re: Need help with this derivative?

    Quote Originally Posted by AFireInside View Post
    Well using the chain rule (x^2+4)^-1 would become -(x^2+4)^-2 x (x^2+4). I don't see how that simplifies things.
    If y(x) = \frac{{f(x)}}{{g(x)}} then y'(x) = \frac{{f'(x)g(x) - f(x)g'(x)}}{{\left[ {g(x)} \right]^2 }}.

    f(x)=3x~\&~g(x)=x^2+4
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  14. #14
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    Re: Need help with this derivative?

    I thought chain rule was nf'(x) x f(x)^n-1
    So it should be -1(2x)(x^+4)^-2
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  15. #15
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    Re: Need help with this derivative?

    Correct, despite the typo, it should be -2x(x^2 + 4)^(-2).

    So now you can apply the product rule.
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