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Thread: differentiation

  1. #1
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    differentiation

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

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

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

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

    Nevermind.

    $\displaystyle y^2=x^4 (1-x)$

    Differentiating :

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

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

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

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


    Divide both sides by $\displaystyle 2 \cdot y$
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