mix=h[3] t[1]+h[2] (-(((E^(c[1])) c[4] t[1])/(c[1]))+(E^(c[1])) t[4])

mix=h[2]t[4]

y=4; x=2;

cox = D[mix, h[x]] /. t[y] -> 0

coy = D[mix, t[y]] /. h[x] -> 0

γ = Coefficient[mix, t[y]h[x]]

rest = mix /. t[y]->0

δ = γ c[y]+(cox /. t->c)

γ c[y]

γ c[y]((E^(-δ)))W