Find the formula for the Laplace transform of the derivative of a function $y^\prime$. Use the initial condition $y(0) = y0$, use $y$ and $y^\prime$ respectively for $y(t)$ and $y^\prime (t)$ and $Y$ for the Laplace transform of $y$.
$\displaystyle L\lbrace y^{\prime}(t)\rbrace(s)=\int_0^\infty e^{-st}y^\prime(t) dt$

$\displaystyle u =$ $dv =$

$\displaystyle du =$ $v =$

$\displaystyle =$ $\Bigg\vert_0^\infty + \displaystyle\int_0^\infty$

$\displaystyle=$