What is laplacetransform te^{10t} ?

The answer to laplacetransform te^{10t} is 1/((s-10)^2)

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laplacetransform te^{10t}

laplace transform

t e^{10 t}

\frac{1}{( s - 10 ) ^{2}}

Solution steps

L {e^{10 t} t}

Use Laplace Transform table:

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

For

t e^{10 t} : f (t) = e^{10 t}, k = 1

= (- 1)^{1} \frac{d}{d s} (L {e^{10 t}})

L {e^{10 t}} : \frac{1}{s - 10}

\frac{d}{d s} (\frac{1}{s - 10}) = - \frac{1}{( s - 10 ) ^{2}}

= (- 1)^{1} (- \frac{1}{( s - 10 ) ^{2}})

= \frac{1}{( s - 10 ) ^{2}}

x \to 0 lim (\frac{( arctan ( 4 x ) )}{ln ( x )})

\frac{\partial}{\partial x} (ln (4 x + 5 y))

x \to 0 + lim (e^{- 2 x} ln (x))

\frac{1}{x}, 3

\frac{1}{2} x y

What is laplacetransform te^{10t} ?
The answer to laplacetransform te^{10t} is 1/((s-10)^2)