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Math Help - differentiation

  1. #1
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    differentiation

    p41 q40
    y = (x^2 ) \sqrt {1-x}
    show that \frac {dy}{dx} = \frac {2y}x - \frac {x^4} { 2y}

    i can only get
    dy / dx = 1/2  x(1-x)^{-1/2}  (4-5x)
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  2. #2
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    Hello,

    Quote Originally Posted by afeasfaerw23231233 View Post
    p41 q40
    y = (x^2 ) \sqrt {1-x}
    show that \frac {dy}{dx} = \frac {2y}x - \frac {x^4} { 2y}

    i can only get
    dy / dx = 1/2  x(1-x)^{-1/2}  (4-5x)
    I don't really understand what you wrote...

    Nevermind.

    y^2=x^4 (1-x)

    Differentiating :

    2 \cdot \frac{dy}{dx} \cdot y=-x^4+4x^3(1-x)

    2 \cdot \frac{dy}{dx} \cdot y=-x^4+4x^3-4x^4

    2 \cdot \frac{dy}{dx} \cdot y=-x^4+4(x^3-x^4)

    2 \cdot \frac{dy}{dx} \cdot y=-x^4+4\cdot \underbrace{(1-x)}_{y^2} \cdot x^3


    Divide both sides by 2 \cdot y
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