1.

x के सापेक्ष ` tan ^(-1)""(4x)/(4-x^(2)) ` का अवकल गुणांक ज्ञात कीजिए|

Answer» माना ` y= tan ^(-1) ""(4x)/( 4-4x^(2)) `
` rArr " "y= tan ^(-1) (x) /(1-(x//2) ^(2)) `
` " "= tan ^(-1) [ (2(x//2))/(1-(x//2)^(2)) ] =2tan ^(-1) ((x)/(2))`
माना ` x//2 =t " "therefore " "y= 2tan ^(-1)(t) `
` therefore(dy)/(dx) =2( d)/(dt) tan ^(-1) t (d)/(dx) ((x)/(2))`
`" "= 2 (1)/(1+t^(2) )*(1)/(2) =(1)/(1+((x)/(x))^(2) )= (4)/(4+x^(2))`


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