Question

`y=sin^(-1)(x/(1+x^2))+cos^(-1)(x/(1+x^2)),` where `0<x<oo`

Answer 1

From tringular conversions,
`y=sin^(-1)((x)/(sqrt(1+x^(2))))+cos^(-1)((1)/(sqrt(1+x^(2))))`
`=tan^(-1)x+tan^(-1)x=2 tan^(-)x`
`therefore" "(dy)/(dx)=(2)/(1+x^(2))`