derivative of (6x^3-2/(x^2-4))

解答

\frac{d}{d x} (\frac{6 x ^{3} - 2}{x ^{2} - 4})

\frac{6 x ^{4} - 72 x ^{2} + 4 x}{( x ^{2} - 4 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{6 x ^{3} - 2}{x ^{2} - 4})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 6 x ^{3} - 2 ) ( x ^{2} - 4 ) - \frac{d}{d x} ( x ^{2} - 4 ) ( 6 x ^{3} - 2 )}{( x ^{2} - 4 ) ^{2}}

\frac{d}{d x} (6 x^{3} - 2) = 18 x^{2}

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

= \frac{18 x ^{2} ( x ^{2} - 4 ) - 2 x ( 6 x ^{3} - 2 )}{( x ^{2} - 4 ) ^{2}}

乘开

18 x^{2} (x^{2} - 4) - 2 x (6 x^{3} - 2) : 6 x^{4} - 72 x^{2} + 4 x

= \frac{6 x ^{4} - 72 x ^{2} + 4 x}{( x ^{2} - 4 ) ^{2}}

t an g e n t f (x) = x^{2} + x

\int sec (5 x) tan (5 x) d x

\frac{d}{d x} (sec (\frac{1}{x}))

x \to 1 lim (- 1)

\int \frac{32 r ^{7} d r}{2 - r ^{8}} d x