Question

How do you find the derivative of `x^2*tan^-1 x`?

Answer 1

`(x^2)/(1+x^2)+2xtan^-1x`

Explanation:

Differentiate using the `color(blue)" product rule "`

• If f(x) = g(x).h(x) then f'(x) = g(x).h'(x) + h(x).g'(x)
`"---------------------------------------------------------"`
here `g(x)=x^2rArrg'(x)=2x`

and `h(x)=tan^-1xrArrh'(x)=1/(1+x^2)`
`"---------------------------------------------------------"`
Substitute these values into f'(x)

`rArrf'(x)=x^2 1/(1+x^2)+tan^-1x.2x`

`=x^2/(1+x^2)+2xtan^-1x`