# Commutation of differentiation and averaging operations

1. ### plasmoid

15
I've been studying Turbulence, and there's a lot of averaging of differential equations involved. The books I've seen remark offhandedly that differentiation and averaging commute

for eg. < $$\frac{df}{dt}$$ > = $$\frac{d<f>}{dt}$$

Here < > is temporal averaging. If the differentiation is w.r.t. a spatial coordinate it makes sense, but could someone help me with the above equation?

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