Macloran expantions

[autumn shell]

I need to expand this to the third derivitive(third order). It is for a friend that has been stuck with this problem for a while. We discussed about using det macloren expantion for arctan and then find f(0), f'(0) and so on for the ln(1-3x) part.

[opaque dune]

The MacLaurin expansion of third order is given by
$$p(x)=f(0)+f'(0)x+\frac{f''(0)x^2}{2}+\frac{f'''(0)x^3}{6}$$
Useful facts for your friend is that $\frac{d}{dx}[arctan(x)]=\frac{1}{1+x^2}$ and $\frac{d}{dx}[ln(x)]=\frac{1}{x}$. Also, don't forget the chain rule.