P: 3,173 I want to prove the next assertion in Jeffrey M. Lee's Manifolds and differential geometry. If $\mathcal{D}_1, \mathcal{D}_2$ are (natural) graded derivations of degrees $r_1,r_2$ respectively, then the operator: $[\mathcal{D}_1,\mathcal{D}_2] := \mathcal{D}_1 \circ \mathcal{D}_2 - (-1)^{r_1 r_2} \mathcal{D}_2 \circ \mathcal{D}_1$ is a natural graded derivation of degree $r_1+r_2$. I am finding it difficult to prove property 2 and 3 of graded derivation for this bracket. Property 2 is given in the next page in definition 1. I am uploading scans of my work (hopefully my hand written work won't stir you away). Attached Thumbnails