How do you differentiate $f(x)=x(arctanx)^2$ ?

Question

2977 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-03-05T03:45:31

I would use the Product Rule for the product between $x$ and $arctan$ and the Chain Rule for the $arctan^2(x)$ .

So you get:

$f'(x)=1*arctan^2(x)+x*2arctan(x)*(1/(1+x^2))=$
$=arctan(x)[arctan(x)+(2x)/(1+x^2)]$

How do you differentiate f(x)=x(arctanx)^2f(x)=x(arctanx)^2?