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Math Help - Derivative of 3x^2+6x+5/Sqrt(x)

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    Derivative of 3x^2+6x+5/Sqrt(x)

    How do I solve this?
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    Re: Derivative of 3x^2+6x+5/Sqrt(x)

    Quote Originally Posted by rhcprule3 View Post
    How do I solve this?
    First of all is this
    3x^2 + 6x + \frac{5}{\sqrt{x}}

    or
    \frac{3x^2 + 6x + 5}{\sqrt{x}}

    -Dan
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    Re: Derivative of 3x^2+6x+5/Sqrt(x)

    in any case just use the formula d(x^n)/dx = nx^(n-1) also remember derivative of sum or difference of functions is sum or difference of derivatives. ie., ( u+/- v)' = u' +/ - v'
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    Re: Derivative of 3x^2+6x+5/Sqrt(x)

    So for the deivative I would get 6x+6-5/2(x^(-7/2))?
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    Re: Derivative of 3x^2+6x+5/Sqrt(x)

    the question is (3x^2+6x+5)/(Sqrt(x))
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    Re: Derivative of 3x^2+6x+5/Sqrt(x)

    Your answer is not right. You can approach this in either of two ways:

    1. Divide the denominator into the numerator to get  f(x) = 3 x^{3/2} + 6x^{1/2} + 5x^{-1/2} Now get the derivative using the same techniques as in your other posts, where the derivative of  x^n is n x^{n-1}.

    2. Use the formula for derivates of one function divided by another: the derivative of  \frac {f(x)}{g(x)} is:  \frac {f'(x) g(x) - f(x)g'(x)}{(g(x))^2}. Here  f(x) = 3x^2+6x+5 and  g(x) = x^{1/2}.

    Both approaches give the same answer.
    Last edited by ebaines; October 3rd 2013 at 09:28 AM.
    Thanks from rhcprule3
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    Re: Derivative of 3x^2+6x+5/Sqrt(x)

    thanks. man i cant believe i didnt even think of that, brainfart i guess...
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