If
F(x) = f(xf(xf(x))),
where
f(1) = 4, f(4) = 6, f '(1) = 4, f '(4) = 5,
and
f '(6) = 6,
find
F '(1).
F' = f'(xf(xf))*(f(xf)+xf'(xf)(f+f(xf')))
= f'(f(f(1)) * (f(f(1))+f'(xf(1))(f(1)+f(f'(1)))
= f'(f(4))*(f(4)+f'(4)(4+f(4)))
= f'(6)(6+5(4+6))
= 6(6+50)
= 6*56
= 336