derivative (ln(t))/t

解

導関数

\frac{ln ( t )}{t}

\frac{1 - ln ( t )}{t ^{2}}

解答ステップ

\frac{d}{d t} (\frac{ln ( t )}{t})

商の法則を適用:

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

= \frac{\frac{d}{d t} ( ln ( t ) ) t - \frac{d t}{d t} ln ( t )}{t ^{2}}

\frac{d}{d t} (ln (t)) = \frac{1}{t}

\frac{d t}{d t} = 1

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

簡素化

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

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