In general, if f(x)=g(x^n) find the "k-th" derivative of f(x) at 0 in terms of the derivatives of g at 0.

Note, this is part c) of a question in which part a) was

prove the taylor polynomial of sin(x^2) of degree 4n+2 at 0 is
<br /> (x^2)+...+(-1)^n[x^{4n+2}]/[(2n+1)!]<br /> hint: if P(x) is the taylor polynomial of degree 2n+1 for sin(x) at 0 then sin(x)=P(x)+R(x) where the lim as x->0 of R(x)/(x^{2n+1}) is 0. what does this imply about the limit as x->0 of R(x^2)/(x^{4n+2}) ?

and part b) was
find the "k-th" derivative of sin(x^2) at 0 for all k.