d/(dt)(xy(t){z}(t))

解

\frac{d}{d t} (x y (t) z (t))

\frac{d x}{d t} y (t) z (t) + (\frac{d}{d t} (y (t)) z (t) + \frac{d}{d t} (z (t)) y (t)) x

解答ステップ

\frac{d}{d t} (x y (t) z (t))

積の法則を適用:

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

f = x, g = y (t) z (t)

= \frac{d x}{d t} y (t) z (t) + \frac{d}{d t} (y (t) z (t)) x

\frac{d}{d t} (y (t) z (t)) = \frac{d}{d t} (y (t)) z (t) + \frac{d}{d t} (z (t)) y (t)

= \frac{d x}{d t} y (t) z (t) + (\frac{d}{d t} (y (t)) z (t) + \frac{d}{d t} (z (t)) y (t)) x