derivative (t^2)/(t-11)

解

導関数

\frac{t ^{2}}{t - 11}

\frac{t ^{2} - 22 t}{( t - 11 ) ^{2}}

解答ステップ

\frac{d}{d t} (\frac{t ^{2}}{t - 11})

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 ^{2} ) ( t - 11 ) - \frac{d}{d t} ( t - 11 ) t ^{2}}{( t - 11 ) ^{2}}

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

\frac{d}{d t} (t - 11) = 1

= \frac{2 t ( t - 11 ) - 1 \cdot t ^{2}}{( t - 11 ) ^{2}}

簡素化

\frac{2 t ( t - 11 ) - 1 \cdot t ^{2}}{( t - 11 ) ^{2}} : \frac{t ^{2} - 22 t}{( t - 11 ) ^{2}}

= \frac{t ^{2} - 22 t}{( t - 11 ) ^{2}}