derivative f(x)=8x(x^2+3)^3

解答

导数

f (x) = 8 x (x^{2} + 3)^{3}

8 ((x^{2} + 3)^{3} + 6 x^{2} (x^{2} + 3)^{2})

求解步骤

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

将常数提出:

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

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

使用微分乘法定则:

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

f = x, g = (x^{2} + 3)^{3}

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

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

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

= 8 (1 \cdot (x^{2} + 3)^{3} + 6 x (x^{2} + 3)^{2} x)

化简

8 (1 \cdot (x^{2} + 3)^{3} + 6 x (x^{2} + 3)^{2} x) : 8 ((x^{2} + 3)^{3} + 6 x^{2} (x^{2} + 3)^{2})

= 8 ((x^{2} + 3)^{3} + 6 x^{2} (x^{2} + 3)^{2})

d er i v a t i v e sin^{8} (x)

\int \frac{e ^{2 x}}{4} d x

\frac{\partial}{\partial x} (x y^{2} e^{3 x^{2} y - y^{2}})

d er i v a t i v e \frac{( x + x )}{x ^{2}}

in v erse l a pl a ce \frac{8}{s - 1} - \frac{3}{s}