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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