d/(dt)((x)(at-asin(t)))

解

\frac{d}{d t} ((x) (a t - a sin (t)))

x (a - a cos (t))

解答ステップ

\frac{d}{d t} ((x) (a t - a sin (t)))

a, x

を定数として扱う

定数を除去:

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

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

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d t} (a t) = a

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

= x (a - a cos (t))