derivative of 18x(x^2+6^8)

解答

\frac{d}{d x} (18 x (x^{2} + 6)^{8})

18 ((x^{2} + 6)^{8} + 16 x^{2} (x^{2} + 6)^{7})

求解步骤

\frac{d}{d x} (18 x (x^{2} + 6)^{8})

将常数提出:

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

= 18 \frac{d}{d x} (x (x^{2} + 6)^{8})

使用微分乘法定则:

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

f = x, g = (x^{2} + 6)^{8}

= 18 (\frac{d x}{d x} (x^{2} + 6)^{8} + \frac{d}{d x} ((x^{2} + 6)^{8}) x)

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

\frac{d}{d x} ((x^{2} + 6)^{8}) = 16 x (x^{2} + 6)^{7}

= 18 (1 \cdot (x^{2} + 6)^{8} + 16 x (x^{2} + 6)^{7} x)

化简

18 (1 \cdot (x^{2} + 6)^{8} + 16 x (x^{2} + 6)^{7} x) : 18 ((x^{2} + 6)^{8} + 16 x^{2} (x^{2} + 6)^{7})

= 18 ((x^{2} + 6)^{8} + 16 x^{2} (x^{2} + 6)^{7})

\int x^{1.5} d x

\int_{0}^{y} 2 d x

\int (x + 1) \cdot e^{x} d x

x \to \infty lim (\frac{lo g _{2} ( lo g _{2} ( x ) )}{2 lo g _{2} ( x )})

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