derivative of (x^4+x-7(2x^3+1))

解答

\frac{d}{d x} ((x^{4} + x - 7) (2 x^{3} + 1))

14 x^{6} + 12 x^{3} - 42 x^{2} + 1

求解步骤

\frac{d}{d x} ((x^{4} + x - 7) (2 x^{3} + 1))

使用微分乘法定则:

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

f = x^{4} + x - 7, g = 2 x^{3} + 1

= \frac{d}{d x} (x^{4} + x - 7) (2 x^{3} + 1) + \frac{d}{d x} (2 x^{3} + 1) (x^{4} + x - 7)

\frac{d}{d x} (x^{4} + x - 7) = 4 x^{3} + 1

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

= (4 x^{3} + 1) (2 x^{3} + 1) + 6 x^{2} (x^{4} + x - 7)

化简

(4 x^{3} + 1) (2 x^{3} + 1) + 6 x^{2} (x^{4} + x - 7) : 14 x^{6} + 12 x^{3} - 42 x^{2} + 1

= 14 x^{6} + 12 x^{3} - 42 x^{2} + 1

x \to 0 - lim (x^{2} - 2 ln (x))

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

a re a x^{2} + 2 x + 2, 3 x + 8, [0, 2]

x \to 2 lim (x^{2} + 5)

\int_{0}^{1} \frac{a x}{x ^{2} - p x} d x