derivative (((x^6)-1))/(((x^6)+1))

解答

导数

\frac{( ( x ^{6} ) - 1 )}{( ( x ^{6} ) + 1 )}

\frac{12 x ^{5}}{( x ^{6} + 1 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x ^{6} - 1}{x ^{6} + 1})

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} ( x ^{6} - 1 ) ( x ^{6} + 1 ) - \frac{d}{d x} ( x ^{6} + 1 ) ( x ^{6} - 1 )}{( x ^{6} + 1 ) ^{2}}

\frac{d}{d x} (x^{6} - 1) = 6 x^{5}

\frac{d}{d x} (x^{6} + 1) = 6 x^{5}

= \frac{6 x ^{5} ( x ^{6} + 1 ) - 6 x ^{5} ( x ^{6} - 1 )}{( x ^{6} + 1 ) ^{2}}

乘开

6 x^{5} (x^{6} + 1) - 6 x^{5} (x^{6} - 1) : 12 x^{5}

= \frac{12 x ^{5}}{( x ^{6} + 1 ) ^{2}}

d er i v a t i v e y = 3 cos (x) + 7 e x + ln (x^{2} + 1)

d er i v a t i v e f (x) = \frac{4 x - 1}{x}

d er i v a t i v e 2^{z}

d er i v a t i v e y = sin (x^{- 1})

d er i v a t i v e x^{2} cos (lo g_{10} (x))