derivative (x^2+4)(2x-6)

解答

导数

(x^{2} + 4) (2 x - 6)

6 x^{2} - 12 x + 8

求解步骤

\frac{d}{d x} ((x^{2} + 4) (2 x - 6))

使用微分乘法定则:

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

f = x^{2} + 4, g = 2 x - 6

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

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

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

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

化简

2 x (2 x - 6) + 2 (x^{2} + 4) : 6 x^{2} - 12 x + 8

= 6 x^{2} - 12 x + 8

t a y l or \frac{1}{( 1 + x ) ^{2}}

\int x^{5} cos (x^{2}) d x

x \to 1 - lim (\frac{7}{1 - x})

\int \frac{x}{1 - 4 x ^{2}} d x

\int \frac{5 x}{( 7 - x ^{2} ) ^{3}} d x