Question

How do you differentiate # f(x) = (1+x^2) arctanx #?

Answer 1

`f'(x)=1+2xtan^-1x`

Explanation:

`"differentiate using the "color(blue)"product rule"`

`"given " f(x)=g(x).h(x)" then"`

`f'(x)=g(x)h'(x)+h(x)g'(x)`

`g(x)=1+x^2rArrg'(x)=2x`

`h(x)=tan^-1xrArrh'(x)=1/(1+x^2)`

`rArrf'(x)=cancel((1+x^2)). 1/cancel((1+x^2))+2xtan^-1x`

`color(white)(rArrf'(x))=1+2xtan^-1x`