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人気のある微分積分 >

derivative of x(1-x^2)

解

\frac{d}{d x} (x (1 - x)^{2})

解

3 x^{2} - 4 x + 1

解答ステップ

\frac{d}{d x} (x (1 - x)^{2})

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (1 - x)^{2}

= \frac{d x}{d x} (1 - x)^{2} + \frac{d}{d x} ((1 - x)^{2}) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((1 - x)^{2}) = - 2 (1 - x)

= 1 \cdot (1 - x)^{2} + (- 2 (1 - x)) x

簡素化

1 \cdot (1 - x)^{2} + (- 2 (1 - x)) x : 3 x^{2} - 4 x + 1

= 3 x^{2} - 4 x + 1

グラフ

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