Prove the chain rule: If ? : D ? W is differentiable in x0 ? D and f : W ? R is differentiable in y0 := ?(x0), then f ? ? : D ? R is differentiable in x0 and (f ? ?) ?(x0) = f(?(x0)) ?(x0) Use the following evidence puzzle pieces for this Put them in a meaningful order and complete the argument

lim f (y) -f(yo) y-+yo y-yo lim $(x) -$(To) T-TO Nach Definition des Differentialquotienten und der Differenzierbarkeit von / in yo und von o in to folgt . o ist stetig, da o is continuous, because . setze y = (x) und yo = $(To) . lim f(o(z))-fo(zo)) T-+TO T-TO . wegen der Stetigkeit von o gilt because of the continuity of . f'(yo) . d'(ro) = f'(o(To)) . d' (To) lim f($ (x) ) - f(0 (20 ) ) . 9(2 ) -6(20) T-TO (7 . After defining the differential quotient and the differentiability of fin yo and of o in x0 it follows