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

解答

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

14 x^{6} - 16 x^{3} - 6

求解步骤

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

使用微分乘法定则:

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

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

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

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

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

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

化简

6 x^{2} (x^{4} - 3 x) + (4 x^{3} - 3) (2 x^{3} + 2) : 14 x^{6} - 16 x^{3} - 6

= 14 x^{6} - 16 x^{3} - 6

t an g e n t f (x) = \frac{x}{1 + x ^{2}}, (3, 0.3)

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