How do you differentiate # f(x) =x^2tan^-1 x #?

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How do you differentiate # f(x) =x^2tan^-1 x #?

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Answer 1 · 2016-11-14T12:44:55

#f'(x)=(x^2\tan^-1(x))'=\color(olive)(x^2/(1+x^2)+2tan^-1(x))#

Explanation:

Apply Product Rule:
#f'(x)=x^2(\tan^-1(x))'+(x^2)'tan^-1(x)#
#=x^2(1/[1+x^2])+2\color(red)(x)(tan^-1(x))#
#=\color(seagreen)(x^2/(1+x^2)+2xtan^-1(x))#

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How do you differentiate # f(x) =x^2tan^-1 x #?

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