d/(ds)(sL({y}(s)))

Lösung

\frac{d}{d s} (s L (y (s)))

L (y (s) + s \frac{d}{d s} (y (s)))

Schritte zur Lösung

\frac{d}{d s} (s L (y (s)))

Entferne die Konstante:

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

= L \frac{d}{d s} (s y (s))

Wende die Produktregel an:

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

f = s, g = y (s)

= L (\frac{d s}{d s} y (s) + \frac{d}{d s} (y (s)) s)

\frac{d s}{d s} = 1

= L (1 \cdot y (s) + \frac{d}{d s} (y (s)) s)

Vereinfache

= L (y (s) + s \frac{d}{d s} (y (s)))

\int \frac{1 + arctan ( x )}{1 + x ^{2}} d x

\frac{\partial}{\partial y} (\frac{1}{2} (x - y)^{2})

x \to 2 lim (x^{2} - 4 x + 2)

in v erse l a pl a ce \frac{1}{2 s ^{2} + s}

\int \frac{1}{x ^{1}} d x