derivative e^{t/9}sin(t/9)

解

導関数

e^{\frac{t}{9}} sin (\frac{t}{9})

e^{\frac{t}{9}} \frac{1}{9} sin (\frac{t}{9}) + cos (\frac{t}{9}) \frac{1}{9} e^{\frac{t}{9}}

解答ステップ

\frac{d}{d t} (e^{\frac{t}{9}} sin (\frac{t}{9}))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{\frac{t}{9}}, g = sin (\frac{t}{9})

= \frac{d}{d t} (e^{\frac{t}{9}}) sin (\frac{t}{9}) + \frac{d}{d t} (sin (\frac{t}{9})) e^{\frac{t}{9}}

\frac{d}{d t} (e^{\frac{t}{9}}) = e^{\frac{t}{9}} \frac{1}{9}

\frac{d}{d t} (sin (\frac{t}{9})) = cos (\frac{t}{9}) \frac{1}{9}

= e^{\frac{t}{9}} \frac{1}{9} sin (\frac{t}{9}) + cos (\frac{t}{9}) \frac{1}{9} e^{\frac{t}{9}}