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Thread: 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)
    $\displaystyle y^{\frac{2}{3}} = 5 - x^{\frac{2}{3}}$

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

    By the chain rule:

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

    $\displaystyle
    =-\frac{\sqrt{5-x^{\frac{2}{3}}}}{\sqrt[3]{x}}$

    $\displaystyle f'(8) =-\frac{\sqrt{5-8^{\frac{2}{3}}}}{\sqrt[3]{8}} = -\frac{1}{2}$
    Last edited by e^(i*pi); Sep 26th 2009 at 01:49 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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