d/(dt)((x)(2acos(t)-acos(2t))dt)

解

\frac{d}{d t} ((x) (2 a cos (t) - a cos (2 t)) d t)

x d (t (- 2 a sin (t) + 2 a sin (2 t)) + 2 a cos (t) - a cos (2 t))

解答ステップ

\frac{d}{d t} ((x) (2 a cos (t) - a cos (2 t)) d t)

a, x, d

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= x d \frac{d}{d t} ((2 a cos (t) - a cos (2 t)) t)

積の法則を適用:

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

f = 2 a cos (t) - a cos (2 t), g = t

= x d (\frac{d}{d t} (2 a cos (t) - a cos (2 t)) t + \frac{d t}{d t} (2 a cos (t) - a cos (2 t)))

\frac{d}{d t} (2 a cos (t) - a cos (2 t)) = - 2 a sin (t) + 2 a sin (2 t)

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

= x d ((- 2 a sin (t) + 2 a sin (2 t)) t + 1 \cdot (2 a cos (t) - a cos (2 t)))

簡素化

= x d (t (- 2 a sin (t) + 2 a sin (2 t)) + 2 a cos (t) - a cos (2 t))