Functional study shows copper deposit in thick skin (8)
I believe the answer is:
calculus
'functional study' is the definition.
'copper deposit in thick skin' is the wordplay.
'copper' becomes 'cu' (chemical symbol).
'deposit in' means one lot of letters goes inside another.
'thick skin' becomes 'callus'.
'cu' going within 'callus' is 'CALCULUS'.
'shows' acts as a link.
(Other definitions for calculus that I've seen before include "method of reasoning" , "Maths with derivatives" , "Maths dealing with rates of variation" , "Branch of mathematics developed by Newton and Leibnitz" , "Hard bit one may find painful" .)