d/(dt)((s(t))(4t^2-6t-5))

解

\frac{d}{d t} ((s (t)) (4 t^{2} - 6 t - 5))

s (12 t^{2} - 12 t - 5)

解答ステップ

\frac{d}{d t} ((s (t)) (4 t^{2} - 6 t - 5))

定数を除去:

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

= s \frac{d}{d t} (t (4 t^{2} - 6 t - 5))

積の法則を適用:

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

f = t, g = 4 t^{2} - 6 t - 5

= s (\frac{d t}{d t} (4 t^{2} - 6 t - 5) + \frac{d}{d t} (4 t^{2} - 6 t - 5) t)

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

\frac{d}{d t} (4 t^{2} - 6 t - 5) = 8 t - 6

= s (1 \cdot (4 t^{2} - 6 t - 5) + (8 t - 6) t)

簡素化

s (1 \cdot (4 t^{2} - 6 t - 5) + (8 t - 6) t) : s (12 t^{2} - 12 t - 5)

= s (12 t^{2} - 12 t - 5)