d/(ds)(s^2{y}(s)-1)

Lösung

\frac{d}{d s} (s^{2} y (s) - 1)

s^{2} \frac{d}{d s} (y (s)) + 2 s y (s)

Schritte zur Lösung

\frac{d}{d s} (s^{2} y (s) - 1)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d s} (s^{2} y (s)) - \frac{d}{d s} (1)

\frac{d}{d s} (s^{2} y (s)) = 2 s y (s) + \frac{d}{d s} (y (s)) s^{2}

\frac{d}{d s} (1) = 0

= 2 s y (s) + \frac{d}{d s} (y (s)) s^{2} - 0

Vereinfache

= s^{2} \frac{d}{d s} (y (s)) + 2 s y (s)

d er i v a t i v e f (x) = x^{2} - 2 x + 1

d er i v a t i v e 6 t - \frac{2}{t}

\frac{d}{d x} (\frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 6 x)

in v erse l a pl a ce \frac{3 s + 17}{s ^{2} + s + 1}

t^{2} y^{^{''}} + 19 t y^{^{'}} + 106 y = 0