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

解答

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

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

求解步骤

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

化简

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

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

使用连锁律:

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

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

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

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

化简

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

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

\int 2 tan^{4} (x) sec^{6} (x) d x

\frac{d y}{d x} = (1 - y) y - 6

in v erse l a pl a ce \frac{1}{2} - \frac{1}{2} \cdot (\frac{1}{s + 1})

\int e^{l n (2 x)} d x

x \to 0 lim (\frac{5 x cot ( 3 x )}{2 sec ( x )})