derivative x^2(1-2x)

解答

导数

x^{2} (1 - 2 x)

2 x - 6 x^{2}

求解步骤

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

使用微分乘法定则:

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

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

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

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

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

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

化简

2 x (1 - 2 x) + (- 2) x^{2} : 2 x - 6 x^{2}

= 2 x - 6 x^{2}

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

\frac{d}{d x} ((4 x - 1)^{2})

a re a y = x^{2}, y = 2 x^{2} - 4 x, y = 0

\int \frac{x ^{2}}{( x ^{2} + 8 ) ^{\frac{3}{2}}} d x

t an g e n t x^{3} - 8 x