derivative (3x^2-x-4)(-x^2+2)

解答

导数

(3 x^{2} - x - 4) (- x^{2} + 2)

- 12 x^{3} + 3 x^{2} + 20 x - 2

求解步骤

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

使用微分乘法定则:

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

f = 3 x^{2} - x - 4, g = - x^{2} + 2

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

\frac{d}{d x} (3 x^{2} - x - 4) = 6 x - 1

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

= (6 x - 1) (- x^{2} + 2) + (- 2 x) (3 x^{2} - x - 4)

化简

(6 x - 1) (- x^{2} + 2) + (- 2 x) (3 x^{2} - x - 4) : - 12 x^{3} + 3 x^{2} + 20 x - 2

= - 12 x^{3} + 3 x^{2} + 20 x - 2

x \to 0 lim (6 x - ln (6 x + 1))

y^{^{''}} + 16 y = t e^{t} cos (4 t)

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

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

y^{^{''}} - 5 y^{^{'}} = 25 t