derivative of ((-x^2-1)/((x^2-1)^2))

解答

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

- \frac{2 x ( - x ^{2} - 3 )}{( x ^{2} - 1 ) ^{3}}

求解步骤

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

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

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

\frac{d}{d x} ((x^{2} - 1)^{2}) = 4 x (x^{2} - 1)

= \frac{( - 2 x ) ( x ^{2} - 1 ) ^{2} - 4 x ( x ^{2} - 1 ) ( - x ^{2} - 1 )}{( ( x ^{2} - 1 ) ^{2} ) ^{2}}

化简

\frac{( - 2 x ) ( x ^{2} - 1 ) ^{2} - 4 x ( x ^{2} - 1 ) ( - x ^{2} - 1 )}{( ( x ^{2} - 1 ) ^{2} ) ^{2}} : - \frac{2 x ( - x ^{2} - 3 )}{( x ^{2} - 1 ) ^{3}}

= - \frac{2 x ( - x ^{2} - 3 )}{( x ^{2} - 1 ) ^{3}}

\int 3 x^{- 1} d x

2 x y d x + (x^{2} - 1) d y = 0

f (x) = \frac{cos ( x )}{1 + sin ( x )}

\frac{\partial}{\partial x} (x^{2} y + y^{3})

a re a - x^{2} + 1.907, 0, 0.266