derivative (log_{e}(x))/(x^2)

解

導関数

\frac{lo g _{e} ( x )}{x ^{2}}

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

解答ステップ

\frac{d}{d x} (\frac{lo g _{e} ( 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} ( lo g _{e} ( x ) ) x ^{2} - \frac{d}{d x} ( x ^{2} ) lo g _{e} ( x )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (lo g_{e} (x)) = \frac{1}{x}

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

= \frac{\frac{1}{x} x ^{2} - 2 x lo g _{e} ( x )}{( x ^{2} ) ^{2}}

簡素化

\frac{\frac{1}{x} x ^{2} - 2 x lo g _{e} ( x )}{( x ^{2} ) ^{2}} : \frac{1 - 2 ln ( x )}{x ^{3}}

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