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

1 Answer
Jim G.
Jun 25, 2017

#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#

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