derivative 10x(x^2+7)^4

解答

导数

10 x (x^{2} + 7)^{4}

10 ((x^{2} + 7)^{4} + 8 x^{2} (x^{2} + 7)^{3})

求解步骤

\frac{d}{d x} (10 x (x^{2} + 7)^{4})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 10 \frac{d}{d x} (x (x^{2} + 7)^{4})

使用微分乘法定则:

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

f = x, g = (x^{2} + 7)^{4}

= 10 (\frac{d x}{d x} (x^{2} + 7)^{4} + \frac{d}{d x} ((x^{2} + 7)^{4}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} ((x^{2} + 7)^{4}) = 8 x (x^{2} + 7)^{3}

= 10 (1 \cdot (x^{2} + 7)^{4} + 8 x (x^{2} + 7)^{3} x)

化简

10 (1 \cdot (x^{2} + 7)^{4} + 8 x (x^{2} + 7)^{3} x) : 10 ((x^{2} + 7)^{4} + 8 x^{2} (x^{2} + 7)^{3})

= 10 ((x^{2} + 7)^{4} + 8 x^{2} (x^{2} + 7)^{3})

(\frac{x + 4}{x - 4})^{5}

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

n = 4 \sum \infty \frac{8}{n ^{2} - 1}

2 x^{2}, 2 x + 6, - 1, 0

x y + 4 y = 10