Deriving spatial derivatives

slurms
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Homework Statement
I'm trying to derive the various spatial derivatives, and find that I'm missing pieces. I'd like another set of eyes please.
Relevant Equations
div, grad, curl, grad^2
See photo. First, I see that I get more standard results by crossing theta before phi. What's the importance of that? Also I'd get more standard results by allowing some r or sine factors to leave their derivative enclosures and unify.
 

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