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

Answer» यहाँ ` y= cot ^(-1) (sqrt(1+x^(2) +x))`
माना ` x=cot theta ` तब
` " "= cot ^(-1) (cosec theta+ cot theta ) =cot ^(-1) ((1)/(sin theta )+(cos theta )/(sin theta))`
` =cot ^(-1) ((1+ costheta )/(sin theta ))=cot^(-1) {(2cos ^(2)(theta //2))/(2sin (theta //2)cos (theta //2))}`
` =cot ^(-1) (cot ""(theta )/(2) )_=(theta)/(2)`
` y= (1)/(2) cot ^(-1) x `
` therefore (dy)/(dx) =(d)/(dx) ((1)/(2)cot ^(-1) x )=(1)/(2) (d)/(dx) (cot ^(-1) x) = (-1)/(2(1+x^(2)))`


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