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

解答

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

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

求解步骤

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

使用连锁律:

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

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

\frac{d}{d x} (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}}}

t an g e n t f (x) = x, (49, 7)

d er i v a t i v e \frac{4 x}{5 - cot ( x )}

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

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

\frac{d}{d x} (- x - \frac{16}{x})