Derivative problem

Sep 2008
222
0
f'(a)=b and f(a)=a; let g(x)=f(f(f(x))). Find g'(a).

This is what I got. If there's anything wrong, please point it out.

g'(x)=[f'(f(f(x)))] [f'(f(x))] [f'(x)]

because f'(a)=b f(a)=a

therefore,

g'(a)= [f'(f(f(a)))] [f'(f(a))] [f'(a)]
= [f'(f(a))] [f'(a)]
= f['(a) ]
= (b) (b) (b)
= b^3