यदि ` y = sin^(-1) ( (2x)/(1+x^(2)))` तो `(dy)/(dx)` ज्ञात कीजिए ।

Explanation

मान लो ` x= tan theta ,` तब ` y = sin^(-1) ((2x)/(1+x^(2))) `
` = sin ^(-1) ((2 tan theta)/(1+ tan^(2) theta))`
` sin^(-1) (sin 2 theta) = 2 theta `
` = 2 tan ^(-1) x`
अतः `(dy)/(dx) = 2 xx 1/( 1+x^(2)) - 2/(1+x^(2))`