Question

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

Answer 1

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)]`