d/(dt)(y+{v}(t)t+(a/2)t^2)

解

\frac{d}{d t} (y + v (t) \cdot t + (\frac{a}{2}) \cdot t^{2})

\frac{d y}{d t} + v (t) + t \frac{d}{d t} (v (t)) + a t

解答ステップ

\frac{d}{d t} (y + v (t) t + (\frac{a}{2}) t^{2})

簡素化

y + v (t) t + (\frac{a}{2}) t^{2} : y + t v (t) + \frac{a t ^{2}}{2}

= \frac{d}{d t} (y + t v (t) + \frac{a t ^{2}}{2})

和/差の法則を適用:

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

= \frac{d y}{d t} + \frac{d}{d t} (t v (t)) + \frac{d}{d t} (\frac{a t ^{2}}{2})

\frac{d}{d t} (t v (t)) = v (t) + t \frac{d}{d t} (v (t))

\frac{d}{d t} (\frac{a t ^{2}}{2}) = a t

= \frac{d y}{d t} + v (t) + t \frac{d}{d t} (v (t)) + a t