derivative of (x^3-2x(-x+6x^2))

解答

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

30 x^{4} - 4 x^{3} - 36 x^{2} + 4 x

求解步骤

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

使用微分乘法定则:

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

f = x^{3} - 2 x, g = - x + 6 x^{2}

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

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

\frac{d}{d x} (- x + 6 x^{2}) = - 1 + 12 x

= (3 x^{2} - 2) (- x + 6 x^{2}) + (- 1 + 12 x) (x^{3} - 2 x)

化简

(3 x^{2} - 2) (- x + 6 x^{2}) + (- 1 + 12 x) (x^{3} - 2 x) : 30 x^{4} - 4 x^{3} - 36 x^{2} + 4 x

= 30 x^{4} - 4 x^{3} - 36 x^{2} + 4 x

(e^{2 x} + 9) \frac{d y}{d x} = y

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

d er i v a t i v e f (x) = (- 25 x^{2} + 1)^{2}

\int \frac{1}{3} cos (3 x) d x

(y^{3} - 1) e^{x} d x + 3 y^{2} (e^{x} + 1) d y = 0, y (0) = 0