Lie algebra: symmetric and exterior power of representation

Question

If $\mathfrak{g}$ is a Lie algebra, $V$ and $W$ are representation of $\mathfrak{g}$ we define the action of $\mathfrak{g}$ on $V \otimes W$ in the following way: $X \cdot (v \otimes w)=(X \cdot v) \otimes w+v \otimes (X \cdot w)$. But how can we define the action of $\mathfrak{g}$ on $Sym^2V$ and $\Lambda^2V$?