Calculus Problem Help.

Suppose f is differentiable and that there are points x1 and x2 such that f(x1)=x2 and f(x2)=x1.
Let g(x) = f(f(f(f(x)))). Show that g'(x1)=g'(x2).

g(x1) = f(f(f(f(x1))))
g(x1) = f(f(f(x2)))
g(x1) = f(f(x1))
g(x1) = f(x2)
g(x1) = x1
g'(x1) = 1

g(x2) = f(f(f(f(x2))))
g(x2) = f(f(f(x1)))
g(x2) = f(f(x2))
g(x2) = f(x1)
g(x2) = x2
g'(x2) = 1

g'(x1) = g'(x2