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人気のある微分積分 >

derivative of x(x-1^3)

解

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

解

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

解答ステップ

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

積の法則を適用:

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

f = x, g = (x - 1)^{3}

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

\frac{d x}{d x} = 1

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

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

簡素化

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

グラフ

人気の例

integral of-x^2(x+1)^3(x-1)

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

(\partial)/(\partial y)(x^2+2y^2)

\frac{\partial}{\partial y} (x^{2} + 2 y^{2})

integral from 0 to 3 of (-x^2+x-1)

\int_{0}^{3} (- x^{2} + x - 1) d x

integral from 1 to 16 of 1/(sqrt(x))

\int_{1}^{16} \frac{1}{x} d x

integral of (2x)/(3(x^2+1))

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