d/(dt)((x)(xsin(wt+c)))

解

\frac{d}{d t} ((x) (x sin (wt + c)))

x^{2} cos (wt + c) w

解答ステップ

\frac{d}{d t} ((x) (x sin (wt + c)))

簡素化

(x) (x sin (wt + c)) : x^{2} sin (wt + c)

= \frac{d}{d t} (x^{2} sin (wt + c))

c, x, w

を定数として扱う

定数を除去:

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

= x^{2} \frac{d}{d t} (sin (wt + c))

連鎖法則を適用:

cos (wt + c) \frac{d}{d t} (wt + c)

= cos (wt + c) \frac{d}{d t} (wt + c)

\frac{d}{d t} (wt + c) = w

= x^{2} cos (wt + c) w