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

解

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

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

解答ステップ

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

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

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

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

簡素化

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

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