derivative F(x)=4x^6(x^4-6x)

解答

导数

F (x) = 4 x^{6} (x^{4} - 6 x)

4 (10 x^{9} - 42 x^{6})

求解步骤

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

将常数提出:

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

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

使用微分乘法定则:

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

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

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

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

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

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

乘开

6 x^{5} (x^{4} - 6 x) + (4 x^{3} - 6) x^{6} : 10 x^{9} - 42 x^{6}

= 4 (10 x^{9} - 42 x^{6})

\int (5 x^{3} + 2 x^{2} - 2 x + 1) d x

t a y l or \frac{x}{( 1 - x ^{2} ) ^{\frac{1}{2}}}

\frac{d}{d x} (\frac{2 π}{x})

d er i v a t i v e f (x) = (3 x + 1)^{\frac{1}{2}}

\int x + 5 d x