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人気のある微分積分 >

derivative f(x)=(8(x^3-6x^2+12x))

解

導関数

f (x) = (8 (x^{3} - 6 x^{2} + 12 x))

解

8 (3 x^{2} - 12 x + 12)

解答ステップ

\frac{d}{d x} (8 (x^{3} - 6 x^{2} + 12 x))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{d}{d x} (x^{3} - 6 x^{2} + 12 x)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 8 (\frac{d}{d x} (x^{3}) - \frac{d}{d x} (6 x^{2}) + \frac{d}{d x} (12 x))

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

\frac{d}{d x} (6 x^{2}) = 12 x

\frac{d}{d x} (12 x) = 12

= 8 (3 x^{2} - 12 x + 12)

グラフ

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