derivative y=x^2(x-1)

解答

导数

y = x^{2} (x - 1)

3 x^{2} - 2 x

求解步骤

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

使用微分乘法定则:

(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}

化简

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

= 3 x^{2} - 2 x

\frac{\partial}{\partial x} (x^{7} y^{9} - x^{6} y^{8})

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

t a y l or (- 5 x + 24)^{\frac{3}{2}}

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