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Beliebt Rechnen >

laplacetransform te^{-t}

Lösung

laplace transformation

t e^{- t}

Lösung

\frac{1}{( s + 1 ) ^{2}}

Schritte zur Lösung

L {e^{- t} t}

Wende Laplace-Transformationstabelle an:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

Für

t e^{- t} : f (t) = e^{- t}, k = 1

= (- 1)^{1} \frac{d}{d s} (L {e^{- t}})

L {e^{- t}} : \frac{1}{s + 1}

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

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

= \frac{1}{( s + 1 ) ^{2}}

Beliebte Beispiele

derivative of e^{-2x}-3y

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

derivative of (2x-1/(x+2))

\frac{d}{d x} (\frac{2 x - 1}{x + 2})

integral of ((\sqrt[3]{x}+sqrt(x^5))/x)

\int (\frac{3 x + x ^{5}}{x}) d x

y^{^{'}} = e^{8 x} - 6 x

derivative f(x)=(40t)/(t+2)

d er i v a t i v e f (x) = \frac{40 t}{t + 2}