Productivity is derived from Produce. Produce is a synonym of Afford. Afford is related to Range. 
Do is related to Grow. Grow is related to Become. Root is a type of Become. Carrot is a type of Root. 
Productivity --DerivedFrom--> Produce <--Synonym--> Afford <--RelatedTo--> Range 
Do <--RelatedTo--> Grow <--RelatedTo--> Become <--IsA-- Root <--IsA-- Carrot 