d/(dt)((θ(t))(4.1t+12.6t^2))

解

\frac{d}{d t} ((θ (t)) (4.1 t + 12.6 t^{2}))

θ (37.8 t^{2} + 8.2 t)

解答ステップ

\frac{d}{d t} ((θ (t)) (4.1 t + 12.6 t^{2}))

θ

を定数として扱う

定数を除去:

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

= θ \frac{d}{d t} (t (4.1 t + 12.6 t^{2}))

積の法則を適用:

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

f = t, g = 4.1 t + 12.6 t^{2}

= θ (\frac{d t}{d t} (4.1 t + 12.6 t^{2}) + \frac{d}{d t} (4.1 t + 12.6 t^{2}) t)

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

\frac{d}{d t} (4.1 t + 12.6 t^{2}) = 4.1 + 25.2 t

= θ (1 \cdot (4.1 t + 12.6 t^{2}) + (4.1 + 25.2 t) t)

簡素化

θ (1 \cdot (4.1 t + 12.6 t^{2}) + (4.1 + 25.2 t) t) : θ (37.8 t^{2} + 8.2 t)

= θ (37.8 t^{2} + 8.2 t)