Question

How do i find the derivative of y=arctan ((x^2)+1)?

Answer 1

`(dy)/(dx)=(2x)/(x^4+2x^2+2)`

Explanation:

As `y=arctan(x^2+1)=>x^2+1=tany` and differentiating it

`2x=sec^2y(dy)/(dx)`

i.e. `(dy)/(dx)=(2x)/sec^2y=(2x)/(1+tan^2y)`

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

= `(2x)/(x^4+2x^2+2)`