d/(dt)((s)(6t^5-8t+5))

解

\frac{d}{d t} ((s) (6 t^{5} - 8 t + 5))

s (30 t^{4} - 8)

解答ステップ

\frac{d}{d t} ((s) (6 t^{5} - 8 t + 5))

定数を除去:

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

= s \frac{d}{d t} (6 t^{5} - 8 t + 5)

和/差の法則を適用:

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

= s (\frac{d}{d t} (6 t^{5}) - \frac{d}{d t} (8 t) + \frac{d}{d t} (5))

\frac{d}{d t} (6 t^{5}) = 30 t^{4}

\frac{d}{d t} (8 t) = 8

\frac{d}{d t} (5) = 0

= s (30 t^{4} - 8 + 0)

簡素化

= s (30 t^{4} - 8)