For the evaluation algebra ${mathbf F}[e^{pm x}]_M$, if $M={partial},$ then $$Der_{non}({mathbf F}[e^{pm x}]_M)$$ of the evaluation algebra ${mathbf F}[e^{pm x}]_M$ is found in the paper [15]. For $M={partial, partial^2 },$ we find $Der_{non}({mathbf F}[e^{pm x}]_M))$ of the evaluation algebra ${mathbf F}[e^{pm x}]_M$ in this paper. We show that there is a non-associative algebra which is the direct sum of derivation invariant subspaces.
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