` tan ^(-1) ((2x)/(1-x^(2))) ` का ` cos^(-1) .(1-x^(2))/(1+x^(2))` का सापेक्ष अवकल गुणांक ज्ञात कीजिए ।

Explanation

माना ` y_(1) = tan^(-1_ ((2x)/ (1-x^(2))`
तथा ` Y^(2) = COS^(-1) (1-X^(2))/(1+X^(2)) `
यहाँ हमे ` (dy)/(dt)` ज्ञात करना है ।
` v r % prop tan theta `लेने पर
` y_(1) = tan^(-1) ((2 tan theta)/ (1- tan^(2)theta))`
` = tan ^(-1) ( tan 2 theta) `
` = 2 theta = 2 tan^(-1) x `
तब `(dy_(1))/(dx) = 2* 1/( 1+x^(2))`
तथा ` y_(2) = cos^(-1) (( 1 - tan ^(2) theta)/( 1+ tan^(2) theta))`
तब `y_(2) = cos^(1) ( cos 2 theta) `
` rArr y_(2) = 2 theta = 2 tan ^(-1) x `
` rArr (dy_(2))/(dy_(2)) = 2/(1+x^(2))`
` (dy_(1))/(dy_(2)) = (2/(1+x^(2)))/(2/(1+x^(2)))= 1. `