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人気のある微分積分 >

derivative f(x)=x^3(2x-1)

解

導関数

f (x) = x^{3} (2 x - 1)

解

8 x^{3} - 3 x^{2}

解答ステップ

\frac{d}{d x} (x^{3} (2 x - 1))

積の法則を適用:

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

f = x^{3}, g = 2 x - 1

= \frac{d}{d x} (x^{3}) (2 x - 1) + \frac{d}{d x} (2 x - 1) x^{3}

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

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

= 3 x^{2} (2 x - 1) + 2 x^{3}

簡素化

3 x^{2} (2 x - 1) + 2 x^{3} : 8 x^{3} - 3 x^{2}

= 8 x^{3} - 3 x^{2}

グラフ

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