Question

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

Answer 1

`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))`