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Math Help - dy/dx

  1. #1
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    dy/dx

    and evaluate the derivative at the given point.

    x^(2/3) + y^(2/3)=5 (8,1)
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Nightasylum View Post
    and evaluate the derivative at the given point.

    x^(2/3) + y^(2/3)=5 (8,1)
    y^{\frac{2}{3}} = 5 - x^{\frac{2}{3}}

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

    By the chain rule:

    \frac{dy}{dx} = \frac{3}{2}(5-x^{\frac{2}{3}})^{\frac{1}{2}} \times -\frac{2}{3}x^{-\frac{1}{3}}

    <br />
=-\frac{\sqrt{5-x^{\frac{2}{3}}}}{\sqrt[3]{x}}

    f'(8) =-\frac{\sqrt{5-8^{\frac{2}{3}}}}{\sqrt[3]{8}} = -\frac{1}{2}
    Last edited by e^(i*pi); September 26th 2009 at 02:49 PM. Reason: forgot minus sign >.<
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  3. #3
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    yu sure it wouldnt be - 1/2?
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  4. #4
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    Quote Originally Posted by Nightasylum View Post
    yu sure it wouldnt be - 1/2?
    You're right, it should be -1/2. For whatever reason I didn't see that minus sign >.<

    Edited in the above post now
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