derivative (ln(x)+2)/(x^2)

解

導関数

\frac{ln ( x ) + 2}{x ^{2}}

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

解答ステップ

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

\frac{d}{d x} (ln (x) + 2) = \frac{1}{x}

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

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

簡素化

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

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