derivative ((sqrt(t)-3t))/t

解

導関数

\frac{( t - 3 t )}{t}

- \frac{1}{2 t ^{\frac{3}{2}}}

解答ステップ

\frac{d}{d t} (\frac{t - 3 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} ( t - 3 t ) t - \frac{d t}{d t} ( t - 3 t )}{t ^{2}}

\frac{d}{d t} (t - 3 t) = \frac{1}{2 t} - 3

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

= \frac{( \frac{1}{2 t} - 3 ) t - 1 \cdot ( t - 3 t )}{t ^{2}}

簡素化

\frac{( \frac{1}{2 t} - 3 ) t - 1 \cdot ( t - 3 t )}{t ^{2}} : - \frac{1}{2 t ^{\frac{3}{2}}}

= - \frac{1}{2 t ^{\frac{3}{2}}}