d/(dt)((h(t))(2.8t+2.5))

解

\frac{d}{d t} ((h (t)) (2.8 t + 2.5))

h (5.6 t + 2.5)

解答ステップ

\frac{d}{d t} ((h (t)) (2.8 t + 2.5))

h

を定数として扱う

定数を除去:

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

= h \frac{d}{d t} (t (2.8 t + 2.5))

積の法則を適用:

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

f = t, g = 2.8 t + 2.5

= h (\frac{d t}{d t} (2.8 t + 2.5) + \frac{d}{d t} (2.8 t + 2.5) t)

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

\frac{d}{d t} (2.8 t + 2.5) = 2.8

= h (1 \cdot (2.8 t + 2.5) + 2.8 t)

簡素化

= h (5.6 t + 2.5)