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Math Help - determine derivative 2

  1. #1
    Senior Member euclid2's Avatar
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    determine derivative 2

    determine the derivative of g(x)=\sqrt{x}(2x+3)^2
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  2. #2
    MHF Contributor Amer's Avatar
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    show some work u can use this

    (g.f)' = f'.g + g'.f
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  3. #3
    Senior Member euclid2's Avatar
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    so

    x^{\frac{1}{2}}(2x+3)^2

    \frac{1}{2}x^{\frac{-1}{2}}(2x+3)^2+x^{\frac{1}{2}}(4(2x+3))

    is that how?
    Last edited by euclid2; September 4th 2010 at 06:56 AM.
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    Yes, that's correct.
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  5. #5
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    Quote Originally Posted by euclid2 View Post
    so

    x^{\frac{1}{2}}(2x+3)^2

    \frac{1}{2}x^{\frac{-1}{2}}(2x+3)^2+x^{\frac{1}{2}}(4(2x+3))

    is that how?
    You can clean it up with some factorisation...

    \frac{1}{2}x^{-\frac{1}{2}}(2x + 3)^2 + 4x^{\frac{1}{2}}(2x + 3) = (2x + 3)\left(\frac{2x + 3}{2\sqrt{x}} + 4\sqrt{x}\right)

     = (2x+3)\left(\frac{2x + 3 + 8x}{2\sqrt{x}}\right)

     = \frac{(2x+3)(10x+3)}{2\sqrt{x}}
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