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

解答

导数

\frac{1}{x ^{2} - \frac{1}{2}}

- \frac{8 x}{( 2 x ^{2} - 1 ) ^{2}}

求解步骤

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

- \frac{1}{( x ^{2} - \frac{1}{2} ) ^{2}} \cdot 2 x : - \frac{8 x}{( 2 x ^{2} - 1 ) ^{2}}

= - \frac{8 x}{( 2 x ^{2} - 1 ) ^{2}}

\int \frac{x + 3}{x ^{2} + 25} d x

x \to 6 lim (\frac{1 - x}{6 - x})

\int_{3}^{5} 3 x d x

t a y l or x^{2}

y^{^{'}} - \frac{9}{x} y = \frac{( y ^{4} )}{x ^{16}}, y (1) = 1