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人気のある微分積分 >

derivative f(x)=x^2(x+1)

解

導関数

f (x) = x^{2} (x + 1)

解

3 x^{2} + 2 x

解答ステップ

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

積の法則を適用:

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

f = x^{2}, g = x + 1

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

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

\frac{d}{d x} (x + 1) = 1

= 2 x (x + 1) + 1 \cdot x^{2}

簡素化

2 x (x + 1) + 1 \cdot x^{2} : 3 x^{2} + 2 x

= 3 x^{2} + 2 x

グラフ

人気の例

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d er i v a t i v e f (x) = \frac{2 x ^{2}}{x ^{2} - 2 x - 8}

integral of x/(x^2+2x)

\int \frac{x}{x ^{2} + 2 x} d x

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y^{''}+4y=cos(t)

y^{^{''}} + 4 y = cos (t)

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