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

解

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

\frac{- 2 x + 3}{2 x ^{\frac{5}{2}}}

解答ステップ

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

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

簡素化

\frac{( 1 - \frac{1}{2 x} ) x ^{2} - 2 x ( x - x )}{( x ^{2} ) ^{2}} : \frac{- 2 x + 3}{2 x ^{\frac{5}{2}}}

= \frac{- 2 x + 3}{2 x ^{\frac{5}{2}}}