There are various papers on finding all the derivations of a non-associative algebra and an anti-symmetrized algebra (see [2], [3], [4], [5], [6], [10], [13], [15], [16]). We and all the derivations of the growing algebra WN($e^{{pm}x_1x_2x_3}$, 0, 3)[1] with the set of all right annihilators $T_3$ = ${id,;partial_1,;partial_2,;partial_3}$ in the paper. The dimension of $Der_{non}$(WN($e^{{pm}x_1x_2x_3}$, 0, 3)$_{[1]}$) of the algebra WN($e^{{pm}x_1x_2x_3}$, 0, 3)$_{[1]}$ is one and every derivation of the algebra WN($e^{{pm}x_1x_2x_3}$, 0, 3)$_{[1]}$ is outer. We show that there is a class P of purely outer algebras in this work.