derivative f(t)=(8^{8t})/t

解

導関数

f (t) = \frac{8 ^{8 t}}{t}

\frac{e ^{8 t l n (8)} \cdot 24 ln ( 2 ) t - 1 \cdot 8 ^{8 t}}{t ^{2}}

解答ステップ

\frac{d}{d t} (\frac{8 ^{8 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} ( 8 ^{8 t} ) t - \frac{d t}{d t} 8 ^{8 t}}{t ^{2}}

\frac{d}{d t} (8^{8 t}) = e^{8 t l n (8)} \cdot 24 ln (2)

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

= \frac{e ^{8 t l n (8)} \cdot 24 ln ( 2 ) t - 1 \cdot 8 ^{8 t}}{t ^{2}}