derivative 4x^6(x^4-3x)

解答

导数

4 x^{6} (x^{4} - 3 x)

4 (10 x^{9} - 21 x^{6})

求解步骤

\frac{d}{d x} (4 x^{6} (x^{4} - 3 x))

将常数提出:

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

= 4 \frac{d}{d x} (x^{6} (x^{4} - 3 x))

使用微分乘法定则:

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

f = x^{6}, g = x^{4} - 3 x

= 4 (\frac{d}{d x} (x^{6}) (x^{4} - 3 x) + \frac{d}{d x} (x^{4} - 3 x) x^{6})

\frac{d}{d x} (x^{6}) = 6 x^{5}

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

= 4 (6 x^{5} (x^{4} - 3 x) + (4 x^{3} - 3) x^{6})

乘开

6 x^{5} (x^{4} - 3 x) + (4 x^{3} - 3) x^{6} : 10 x^{9} - 21 x^{6}

= 4 (10 x^{9} - 21 x^{6})

\frac{d}{d x} \frac{( 3 - e ^{\frac{1}{x}} )}{3 + e ^{\frac{1}{x}}}

\frac{\partial}{\partial x} (tan (\frac{x y}{z ^{2}}))

\int \frac{x ^{2} - x - 2}{x ^{3} - 2 x - 4} d x

d er i v a t i v e 4 cos^{4} (x)

d er i v a t i v e y = (2 x^{2} + 5) (4 x - 5)