Differentiation speed as a function of concentration

Concentration c as a function of distance r from the center satisfies

c(r) = 1/r


Distance as a function of time t satisfies

r(t) = (10 - t)^(2/3)


Speed s as a function of time t satisfies

s(t) = -2/3 * (10-t)^(-1/3)

Express the speed as a function of the concentration c.
(as an intermediate step, express the speed as a function of the distance r
itself)

r(t) = (10 - t)^(2/3)
r^3/2 = 10 - t
r^3/2 - 10 = - t
10 - r^3/2 = t

s(r) = s(10 - r^3/2) = -2/3 * (10-(10 - r^3/2))^(-1/3)
Simplify.

r = 1 / c
s(r) = s(1/c) = ...

s(t) = (-2/3) * r^(-1/2) = (-2/3) sqrt(c).