# How do you find the Maclaurin series of f(x)=cos(x^2) ?

cosx=sum_{n=0}^infty(-1)^n{x^{2n}}/{(2n)!}
by replacing $x$ by ${x}^{2}$,
cos(x^2)=sum_{n=0}^infty(-1)^n{x^{4n}}/{(2n)!}