How do you differentiate f(x) =x^2tan^-1 x f(x)=x2tan−1x?

1 Answer
seol
Nov 14, 2016

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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