फलन ` y= log (sqrt ( x) +(1)/(sqrt(x)) ) , ` तब ` (dy)/(dx) ` का मान ज्ञात कीजिए|

Explanation

`y=log (sqrt(x)+ (1)/(sqrt(3))),` माना ` sqrt(x) +(1)/(sqrt(x) ) =t `
` " "therefore " "y= logt `
` therefore " "(dy)/(dx) =(d)/(dt) log t (d)/(dx)(x^(1//2) + x^(-1//2) `
` " "(1)/(t) [ (1)/(2)x^(-1//2)+(-(1)/(2) ) x^(-3//2) ] `
` " "= (1)/(2t) [ (1)/(sqrt(x) ) -(1)/(xsqrt(x)) ] =(1)/(2((x+1)/(sqrt(x)))) [(x-1) /(xsqrt(x) )]`
` " "= ((x-1))/(2x(x+1)) `