((1-2ln(x))/(x^3))^'

解

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

- \frac{- 6 ln ( x ) + 5}{x ^{4}}

解答ステップ

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

商の法則を適用:

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

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

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

(x^{3})^{'} = 3 x^{2}

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

簡素化

\frac{( - \frac{2}{x} ) x ^{3} - 3 x ^{2} ( 1 - 2 ln ( x ) )}{( x ^{3} ) ^{2}} : - \frac{- 6 ln ( x ) + 5}{x ^{4}}

= - \frac{- 6 ln ( x ) + 5}{x ^{4}}