derivative f(t)=(sin(t))/t

解

導関数

f (t) = \frac{sin ( t )}{t}

\frac{t cos ( t ) - sin ( t )}{t ^{2}}

解答ステップ

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

\frac{d}{d t} (sin (t)) = cos (t)

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

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

簡素化

= \frac{t cos ( t ) - sin ( t )}{t ^{2}}