'auxinically' originates from Modern English, specifically formed from the adjective 'auxinic' (derived from 'auxin') with the adverbial suffix '-ally'; 'auxin' ultimately comes from Greek 'auxein', where the root 'aux-' meant 'to grow' or 'to increase'.

'auxin' was coined in English in the early 20th century from Greek 'auxein'; the adjective 'auxinic' developed from 'auxin' + the adjectival suffix '-ic', and the adverb 'auxinically' formed later by adding the adverbial suffix '-ally' to 'auxinic'.

Originally the Greek root meant 'to grow' or 'to increase'; over time 'auxin' became the name for a class of plant hormones that promote growth, and 'auxinically' now means 'in a manner relating to or caused by auxin'.