यदि `y= tan ^(-1) ((sqrt(1+ x^(2))+1)/(x))` तब ` (dy)/(dx)` का मान ज्ञात कीजिए |

Explanation

`y=tan ^(-1) ((sqrt(1+x^(2) )+1) /(x))`

माना ` x tan theta ,` तब

` y= tan ^(-1) ((sectheta +1)/(tan theta ))`

`=tan ^(-1) ((1+costheta )/(sin theta ))`

` =tan ^(-1) { (2cos ^(2) (theta //2))/(2sin (theta //2)cos (theta //2))}`

` =tan ^(-1) {cot ""(theta)/(2) } `

`=tan ^(-1) {tan ((pi)/(2)-(theta )/(2))}`

` =((pi)/(2)-(theta )/(2) )`

`= (pi)/(2) -(1)/(2) tan ^(_1) x `

` therefore " "(dy)/(dx) =-(1)/(2(1+x^(2)))`