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Math Help - Complex Derivative (for me, anyways)

  1. #1
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    Complex Derivative (for me, anyways)

    y= \frac{3}{2}(\sqrt{x}-\frac{1}{\sqrt{x^5}})+\frac{1}{2}(\frac{1}{\sqrt{x  }}-\frac{1}{\sqrt{x^3}})

    So I converted it to:

    \frac{3}{2}(x^{1/2}-x^{-5/2})+\frac{1}{2}(x^{-1/2}-x^{-3/2})

    Then I took the derivative to get:

    \frac{3}{2}(\frac{1}{2}x^{-1/2}+\frac{5}{2}x^{-7/2})+\frac{1}{2}(\frac{-1}{2}x^{-3/2}+\frac{3}{2}x^{-5/2})

    Then I simplified it to:

    \frac{3}{4}(x^{-1/2}+5x^{-7/2})+\frac{1}{4}(-x^{-3/2}+3x^{-5/2})



    This doesn't match the answer in the back of the book, does anyone see any errors? Thank You.
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by dbakeg00 View Post
    y= \frac{3}{2}(\sqrt{x}-\frac{1}{\sqrt{x^5}})+\frac{1}{2}(\frac{1}{\sqrt{x  }}-\frac{1}{\sqrt{x^3}})

    So I converted it to:

    \frac{3}{2}(x^{1/2}-x^{-5/2})+\frac{1}{2}(x^{-1/2}-x^{-3/2})

    Then I took the derivative to get:

    \frac{3}{2}(\frac{1}{2}x^{-1/2}+\frac{5}{2}x^{-7/2})+\frac{1}{2}(\frac{-1}{2}x^{-3/2}+\frac{3}{2}x^{-5/2})

    Then I simplified it to:

    \frac{3}{4}(x^{-1/2}+5x^{-7/2})+\frac{1}{4}(-x^{-3/2}+3x^{-5/2})



    This doesn't match the answer in the back of the book, does anyone see any errors? Thank You.
    That looks fine to me. Perhaps your book has it in a different notation
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  3. #3
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    Quote Originally Posted by e^(i*pi) View Post
    That looks fine to me. Perhaps your book has it in a different notation
    The notation that the book puts the answer in is:

    \frac{3}{4}(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{x^5}  })+\frac{1}{4}(\frac{15}{\sqrt{x^7}}-\frac{1}{\sqrt{x^3}})
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  4. #4
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    Those are are the same, just in different order.
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  5. #5
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    Quote Originally Posted by Plato View Post
    Those are are the same, just in different order.
    I see it now. Thank you. I think this book takes unnecessary steps to put its answers in different forms. I don't see any reason to re order those, but that's just me. Thanks again for the help.
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