d/(dt)((x)(32(t-sin(t))))

解

\frac{d}{d t} ((x) (32 (t - sin (t))))

32 (\frac{d x}{d t} (t - sin (t)) + (1 - cos (t)) x)

解答ステップ

\frac{d}{d t} ((x) (32 (t - sin (t))))

定数を除去:

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

= 32 \frac{d}{d t} (x (t - sin (t)))

積の法則を適用:

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

f = x, g = t - sin (t)

= 32 (\frac{d x}{d t} (t - sin (t)) + \frac{d}{d t} (t - sin (t)) x)

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

= 32 (\frac{d x}{d t} (t - sin (t)) + (1 - cos (t)) x)