(1/(sqrt(1-x^2)))^'

解答

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

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

求解步骤

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

使用指数法则:

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

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

使用连锁律:

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

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

(1 - x^{2})^{'} = - 2 x

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

化简

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

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

y^{^{'}} = 7 y - x

x \to 5 - lim (- (x - 3)^{2})

\int \frac{1}{y ( y - 1 )} d y

\int \frac{x}{8 x ^{2} + 6} d x

ma c l a u r in (1 + x)^{- \frac{7}{3}}