d/(dt)(y/t-(y/t)^2)

解

\frac{d}{d t} (\frac{y}{t} - (\frac{y}{t})^{2})

\frac{t \frac{d y}{d t} - y}{t ^{2}} - \frac{2 y ( t \frac{d y}{d t} - y )}{t ^{3}}

解答ステップ

\frac{d}{d t} (\frac{y}{t} - (\frac{y}{t})^{2})

簡素化

\frac{y}{t} - (\frac{y}{t})^{2} : \frac{y}{t} - \frac{y ^{2}}{t ^{2}}

= \frac{d}{d t} (\frac{y}{t} - \frac{y ^{2}}{t ^{2}})

和/差の法則を適用:

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

= \frac{d}{d t} (\frac{y}{t}) - \frac{d}{d t} (\frac{y ^{2}}{t ^{2}})

\frac{d}{d t} (\frac{y}{t}) = \frac{t \frac{d y}{d t} - y}{t ^{2}}

\frac{d}{d t} (\frac{y ^{2}}{t ^{2}}) = \frac{2 y ( t \frac{d y}{d t} - y )}{t ^{3}}

= \frac{t \frac{d y}{d t} - y}{t ^{2}} - \frac{2 y ( t \frac{d y}{d t} - y )}{t ^{3}}