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

Lösung

\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}}

Schritte zur Lösung

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

Vereinfache

\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}})

Wende die Summen-/Differenzregel an:

(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}}

\int_{1}^{2} \frac{4}{x} - \frac{16}{x ^{2}} d x

\frac{\partial}{\partial y} (y - e^{- 2 x^{2} y})

\frac{\partial}{\partial x} (x (x - 2 y))

\int_{0}^{0.1} x arctan (2 x) d x

\int 14 cot^{4} (x) d x