can someone please help me with the maclaurin series? how do you do this problem??

Question

Find the Maclaurin series for f(x) using the definition of a
Maclaurin series. [Assume that f has a power series expansion. Do not show that Rsubn (x) -> 0.] Also find the associated radius of convergence.
f(x)=sin2x

Answer 1

As in the other cases you've asked, it's easy to find a general formula for the nth derivative of f. It's a lot like the nth derivative of sin(x), except there's an extra factor of 2^n. :)