Math Help - Arctan Maclaurin series

1. Arctan Maclaurin series

Find T4(x), the fourth degree Taylor polynomial of the function f(x)=arctan(13x) at a=0.

I did the work out
got this

13[x-x^3/3+x^5/5-x^7/7.....]

so then 13x- 13x^3/3+13x^5/5-13x^9/9

Since there is no 4th degree, i took -13x^3/3 as the answer, but my online hw says this is incorrect, but this is how my tutor explained it. What's wrong here?

What you did would make sense if $\arctan(13x)=13\arctan(x)$, which it does not. Try instead just writing out the fourth degree polynomial for $\arctan(z)$ and then replacing all the z's by $13x$