Calculating Recursive Derivatives at Point x=0

[Monsu]

hi, could smne pls give me an idea of how to deal with this problem?

Suppose that f(0) = 0 and that f'(0) =1 , calculate f(f(f(x))) at point x=0
thanks a lot, any hint at all would b helpful, as i completely clueless.

 

[vsage]

if f(0) = 0 then f(f(0)) = f(0) = 0.. it's recursive. I am not sure why you would need f'(x) to solve nothing to do with derivatives. Are you sure you typed the question correctly?

 

[Monsu]

here it is again:
f(0) = 0 and f'(0) = 1 calculate the derivative of f(f(f(x))) at point x=0

that's the exact question.
thanks for the help on the second question

 

[vsage]

Oh I see calculate the DERIVATIVE of f(f(f(0)))

First let's set g(x) = f(f(x))
g'(x) is therefore f'(f(x))*f'(x)

Derivative f(g(x)) after substitution is f'(g(x))*g'(x)

= f'(f(f(0)))*f'(f(0))*f'(0)

What a mouthful. If I were to venture a wild crazy guess I'd say that simplifies to 1.

 

[Monsu]

oh great! i just worked it out, it did come to 1. thanks a lot.
can u give a further hint on the other question, I'm still a bit confused there.
thanks again, marvellous!