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

解答

导数

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

5 x^{4} - 15 x^{2} + 6

求解步骤

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

使用微分乘法定则:

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

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

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

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

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

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

化简

2 x (x^{3} - 3 x) + (3 x^{2} - 3) (x^{2} - 2) : 5 x^{4} - 15 x^{2} + 6

= 5 x^{4} - 15 x^{2} + 6

\int \frac{tan ( 3 x )}{cos ( 3 x )} d x

5 y^{^{''}} + y^{^{'}} = - 10 x, y (0) = 0, y^{^{'}} (0) = - 15

t an g e n t f (x) = \frac{2 x + 1}{x + 2}, (1, 1)

\int (x \cdot (1 - x^{4})) d x

\frac{d y}{d x} = y^{2} x^{3}