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

解

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

- \frac{- x + 4}{x ^{3}}

解答ステップ

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

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

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

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

簡素化

\frac{( - 1 ) x ^{2} - 2 x ( 2 - x )}{( x ^{2} ) ^{2}} : - \frac{- x + 4}{x ^{3}}

= - \frac{- x + 4}{x ^{3}}