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人気のある微分積分 >

derivative f(x)=(4x-x^2)^3

解

導関数

f (x) = (4 x - x^{2})^{3}

解

3 (4 x - x^{2})^{2} (4 - 2 x)

解答ステップ

\frac{d}{d x} ((4 x - x^{2})^{3})

連鎖法則を適用:

3 (4 x - x^{2})^{2} \frac{d}{d x} (4 x - x^{2})

= 3 (4 x - x^{2})^{2} \frac{d}{d x} (4 x - x^{2})

\frac{d}{d x} (4 x - x^{2}) = 4 - 2 x

= 3 (4 x - x^{2})^{2} (4 - 2 x)

グラフ

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