# Cubic Power of Supercovariant Derivative

Let $$\bar{D}_{\dot{\alpha}}=\bar{\partial}_{\dot{\alpha}}-i(\bar{\sigma}^{\mu})_{\dot{\alpha}\beta}\theta^{\theta}\partial_{\mu}$$ be the supercovariant derivative. How to prove the following identity?

$$\bar{D}_{\dot{\alpha}}\bar{D}^{2}\equiv0$$

where $$\bar{D}^{2}=\bar{D}^{\dot{\beta}}\bar{D}_{\dot{\beta}}$$.

1. One of the covariant derivatives in $$\bar{D}^{2}$$ must be $$\bar{D}_{\dot{\alpha}}$$.