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

解答

导数

f (x) = x (2 x - 1) (3 x + 2)

18 x^{2} + 2 x - 2

求解步骤

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

使用微分乘法定则:

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

f = x, g = (2 x - 1) (3 x + 2)

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

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

\frac{d}{d x} ((2 x - 1) (3 x + 2)) = 12 x + 1

= 1 \cdot (2 x - 1) (3 x + 2) + (12 x + 1) x

化简

1 \cdot (2 x - 1) (3 x + 2) + (12 x + 1) x : 18 x^{2} + 2 x - 2

= 18 x^{2} + 2 x - 2

\int \frac{x ^{2} ( 3 - x )}{x ^{4} - 4 x ^{3}} d x

\frac{d}{d x} (\frac{e ^{- 2.8 x} - e ^{- 4.6 x}}{1.8})

in v erse l a pl a ce \frac{80}{s ^{2} + 40 s}

\frac{d}{d x} (e^{x} + 2^{- x} + 2 cos (x) - 6)

\int \frac{1}{12 x ^{2}} d x