derivative (2t^2+1)/t

解

導関数

\frac{2 t ^{2} + 1}{t}

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

解答ステップ

\frac{d}{d t} (\frac{2 t ^{2} + 1}{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} ( 2 t ^{2} + 1 ) t - \frac{d t}{d t} ( 2 t ^{2} + 1 )}{t ^{2}}

\frac{d}{d t} (2 t^{2} + 1) = 4 t

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

= \frac{4 tt - 1 \cdot ( 2 t ^{2} + 1 )}{t ^{2}}

簡素化

\frac{4 tt - 1 \cdot ( 2 t ^{2} + 1 )}{t ^{2}} : \frac{2 t ^{2} - 1}{t ^{2}}

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