derivative 1/((x^2-1)(x^2+5x+5))

解答

导数

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

- \frac{4 x ^{3} + 15 x ^{2} + 8 x - 5}{( x ^{2} - 1 ) ^{2} ( x ^{2} + 5 x + 5 ) ^{2}}

求解步骤

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

使用指数法则:

\frac{1}{a} = a^{- 1}

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

使用连锁律:

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

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

\frac{d}{d x} ((x^{2} - 1) (x^{2} + 5 x + 5)) = 4 x^{3} + 15 x^{2} + 8 x - 5

= - \frac{1}{( ( x ^{2} - 1 ) ( x ^{2} + 5 x + 5 ) ) ^{2}} (4 x^{3} + 15 x^{2} + 8 x - 5)

化简

- \frac{1}{( ( x ^{2} - 1 ) ( x ^{2} + 5 x + 5 ) ) ^{2}} (4 x^{3} + 15 x^{2} + 8 x - 5) : - \frac{4 x ^{3} + 15 x ^{2} + 8 x - 5}{( x ^{2} - 1 ) ^{2} ( x ^{2} + 5 x + 5 ) ^{2}}

= - \frac{4 x ^{3} + 15 x ^{2} + 8 x - 5}{( x ^{2} - 1 ) ^{2} ( x ^{2} + 5 x + 5 ) ^{2}}

\int_{0}^{1} (e^{2 x} - e^{- x}) d x

\frac{\partial}{\partial x} (x^{4} - y^{3})

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a re a x^{3} + x^{2}, 2 x^{2} + 2 x

in v erse l a pl a ce cos (w)