In general, if 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 of degree 4n+2 at 0 is

hint: if is the taylor polynomial of degree 2n+1 for sin(x) at 0 then where the lim as x->0 of is 0. what does this imply about the limit as x->0 of ?

and part b) was

find the "k-th" derivative of at 0 for all k.