derivative f(x)=(ln(x^2))/x

解

導関数

f (x) = \frac{ln ( x ^{2} )}{x}

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

解答ステップ

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

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

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

\frac{d x}{d x} = 1

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

簡素化

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

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