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人気のある微分積分 >

derivative f(x)=(2x-x^2)^3

解

導関数

f (x) = (2 x - x^{2})^{3}

解

3 (2 x - x^{2})^{2} (2 - 2 x)

解答ステップ

\frac{d}{d x} ((2 x - x^{2})^{3})

連鎖法則を適用:

3 (2 x - x^{2})^{2} \frac{d}{d x} (2 x - x^{2})

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

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

= 3 (2 x - x^{2})^{2} (2 - 2 x)

グラフ

人気の例

y^{^{'}} = 3 - (2 y)

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