# Using the derivative theorem and, find the Laplace transform of the following functions. r \cos h(t)

Using the derivative theorem and, find the Laplace transform of the following functions
$r\mathrm{cos}h\left(t\right)$
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Laplase transform of $t\mathrm{cos}\left(h\right)t$
$L\left(t\mathrm{cos}\left(h\right)t\right)$
derivative of Laplase transform of $\mathrm{cos}\left(h\right)t$
$\therefore L\left(\mathrm{cos}ht\right)=\frac{s}{{s}^{2}-1}$
$\therefore L\left(t\mathrm{cos}ht\right)=\frac{d}{ds}\frac{s}{{s}^{2}-1}=\frac{{s}^{2}-1-2{s}^{2}}{{\left({s}^{2}-1\right)}^{2}}{\left(-1\right)}^{2}$
$=\frac{-{s}^{2}-1}{{\left({s}^{2}-1\right)}^{2}}\left(-1\right)$
$=\frac{{s}^{2}+1}{{\left({s}^{2}-1\right)}^{2}}$