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

解答

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

\frac{2}{x ^{3}}

求解步骤

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

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

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

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

化简

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

= \frac{2}{x ^{3}}

\int x \cdot e^{x} d x

\frac{d}{d x} (81 + x^{2})

\frac{d}{d x} (x arcsin (\frac{x}{4}) + 16 - x^{2})

\int 45 (1 + x) d x

\frac{\partial}{\partial x} (ln (x^{y}))