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A function $f:ℝ\to ℝ$ is said to have the $n$-th Laplace derivative on the right at $x$ if $f$ is continuous in a right neighborhood of $x$ and there exist real numbers ${\alpha }_0,...,{\alpha }_{n-1}$ such that $s^{n+1}{\int }_0^{\delta }{e}^{-st}[f(x+t)-{\sum }_{i=0}^{n-1}{\alpha }_i{t}^i/i!]dt$ converges as $s\to +\infty$ for some $\delta >0$. There is a corresponding definition on the left. The function is said to have the $n$-th Laplace derivative at $x$ when these two are equal, the common value is denoted by $f_{\langle n\rangle }\left(x\right)$. In this work we establish the basic properties of this new derivative and show that, by an example, it is more general than the generalized...