1.

`sin ^(-1) ((1-x) /(1+x) ) ` का `sqrt(x)` के सापेक्ष अवकल गुणांक ज्ञात कीजिए|

Answer» माना ` y_1=sin ^(-1) ((1-x) /(1+x) ) ` तथा ` " "y_2 sqrt(x) `
` because " "y_1 =sin ^(-1) ((1-x)/(1+x)) `
` therefore " "(dy_1)/(dx ) =(1+x)/(sqrt((1+x )^(2)-(1-x) ^(2) ))*(d)/(dx) ((1-x)/(1+x))`
` " "= ((1+x))/sqrt(4x)*((1+x)(-1)-(1-x)*1)/((1+x)^(2))`
` " "= (-(1+x+1-x))/(2sqrt(x) (1+x)) `
` " " (-2)/(2sqrt(x)(1+x) )=(-1)/(sqrt(x) (1+x))`
` therefore " "(dy_1) /(dx) =(-1)/(sqrt(x) (1+x) ) `
` because " "y_2 =x^(1//2) " "because (dy_2)/(dx)=(1)/(2sqrt(x))`
अतः` (dy_1)/(dy_2) =(y_1 ("का x के सापेक्ष अवकलन")) / (y_2("का x के सापेक्ष अवकलन"))`
` (-1)/((sqrt(x) (1+x))/((1)/(2sqrt(x))))=(-2)/((1+x) )`
` " "therefore (dy_1)/(dy_2) =(-2)/(1+x)`


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