derivative f(t)=te^tcot(t)

解

導関数

f (t) = t e^{t} cot (t)

e^{t} cot (t) + t (e^{t} cot (t) - e^{t} csc^{2} (t))

解答ステップ

\frac{d}{d t} (t e^{t} cot (t))

積の法則を適用:

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

f = t, g = e^{t} cot (t)

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

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

\frac{d}{d t} (e^{t} cot (t)) = e^{t} cot (t) - e^{t} csc^{2} (t)

= 1 \cdot e^{t} cot (t) + (e^{t} cot (t) - e^{t} csc^{2} (t)) t

簡素化

= e^{t} cot (t) + t (e^{t} cot (t) - e^{t} csc^{2} (t))