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人気のある微分積分 >

derivative f(x)=x^3-12x^2+48x

解

導関数

f (x) = x^{3} - 12 x^{2} + 48 x

解

3 x^{2} - 24 x + 48

解答ステップ

\frac{d}{d x} (x^{3} - 12 x^{2} + 48 x)

和/差の法則を適用:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (12 x^{2}) + \frac{d}{d x} (48 x)

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

\frac{d}{d x} (12 x^{2}) = 24 x

\frac{d}{d x} (48 x) = 48

= 3 x^{2} - 24 x + 48

グラフ

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