derivative f(x)=(3x^2+2)(8x^3-3)

解答

导数

f (x) = (3 x^{2} + 2) (8 x^{3} - 3)

120 x^{4} + 48 x^{2} - 18 x

求解步骤

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

使用微分乘法定则:

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

f = 3 x^{2} + 2, g = 8 x^{3} - 3

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

\frac{d}{d x} (3 x^{2} + 2) = 6 x

\frac{d}{d x} (8 x^{3} - 3) = 24 x^{2}

= 6 x (8 x^{3} - 3) + 24 x^{2} (3 x^{2} + 2)

化简

6 x (8 x^{3} - 3) + 24 x^{2} (3 x^{2} + 2) : 120 x^{4} + 48 x^{2} - 18 x

= 120 x^{4} + 48 x^{2} - 18 x

\frac{d y}{d x} = 5 y x

\int \frac{30}{( x + 1 ) ( x ^{2} + 9 ) ^{2}} d x

x \to 1 lim (3 x^{2} + 3 x - 1)

\frac{d}{d x} (\frac{3 x}{f ( x )})

x \to 1 + lim (x^{\frac{1}{x - 1}})