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

Explanation

`y= cot ^(-1) ((1-x )/(1+x))`
माना ` " "x= tan theta `
` y= cot ^(_1) ((1-tan theta )/(1+tan theta )) =cot ^(-1) ""{tan ((pi )/(4) -theta )}`
` " "= cot ^(-1) [ cot {(pi)/(2) - ((pi)/(4)-theta )}]`
` " "= cot^(-1) [cot ""((pi)/(4) +theta )] =(pi)/(4) +theta `
` y= (pi)/(4) +tan ^(-1) x,` जहाँ `x= tan thetarArrtheta tan^(-1) x (dy)/(dx) =(d)/(dx) ((pi)/(4) +tan ^(-1) x)`
` rArr (d)/(dx) ((pi)/(4) )+ (d)/(dx) (tan ^(-1) x ) =0+( 1)/((1+x^(2) )) =(1)/((1+x^(2))`