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    what  \frac{dy}{dx} value is found at point (12,3) on the curve with equation  \frac{x+3}{(2x+1)^\frac{1}{2}}

    Answer \frac{2}{25}

    My answer, i got 5 different answers, so i will just post my working

     \frac{\sqrt{2x+1}+\frac{x+3}{ \sqrt{(2x+1)^3}}}{2x+1} my answers were wrong.
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     \frac{x+3}{(2x+1)^{-\frac{1}{2}}} = (x+3)(2x+1)^{\frac{1}{2}} so it's probably easier to use the product rule instead.

    Using the quotient rule, your first term in the numerator is incorrect: the power should be -1/2, not 1/2. In the denominator, the power should be -1, not 1. Can you see why?
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    The curve should be y= (x+3)/(2x+1)^(1/2) so that (12, 3) lies on it.
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    Oh i didnt even change that power, thanks im goling to try it again.
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    O wait guys, the question i put up is wrong, the power is not  -\frac{1}{2} il change it
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    (Original post by Core)
    O wait guys, the question i put up is wrong, the power is not  -\frac{1}{2} il change it
    Okay. Now that you've corrected it, you can either rewrite it as  (x+3)(2x+1)^{-\frac{1}{2}} and use the product rule, or try the quotient rule again. In light of this correction, your working (that you posted in your OP) is now incorrect only in the second term of the numerator.
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    (Original post by Daniel Freedman)
    Okay. Now that you've corrected it, you can either rewrite it as  (x+3)(2x+1)^{-\frac{1}{2}} and use the product rule, or try the quotient rule again. In light of this correction, your working (that you posted in your OP) is now incorrect only in the second term of the numerator.
    I tried it again using he product rule and i got the right answer, but i want to get the right answer using the qoutient rule since it was in the qoutient chapter.
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    got it using the qoutient rule now  \frac{ \sqrt{25} - \frac{15}{\sqrt{25}}}{25} = \frac{5 - \frac{15}{5}}{25}=\frac{2}{25}
 
 
 

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