निम्न फलन का अवकल गुणांक ज्ञात कीजिये-
` x^(1//x)+ ((1)/(x))^(1//x)`

Answer

` (i) x^(x) (1+log x )+ a^(x) log a +ax^(a-1)(ii) x^(1//x) ((1-log x )/(x^(2)))-((1)/(x))^(1//x)*(1)/(x^(2))(1+log"" (1)/(x)) (iii) (x+ 1)^(2) (x+4)^(3) log x ((2)/(x+1)+(3)/(x+4) + (1)/(xlog x ))(iv) (5^(x) )/(x^(5) )(log 5 -(5)/(x))`

Explanation

(ii )माना ` y= x^(1//x) +((1)/(x))^(1//x) =y_1+y_2 `
जहाँ ` y_1 =x^(1//x) ` और ` y_2 =((1)/(x))^(1//x)`
अब ` " "log y_1 =(1)/(x) log x `
` rArr " "(dy_1)/(dx)= x^(1//x) ((1-logx )/(x^(2)))` व ` log y_2 =(1)/(x) log ""(1)/(x)`
` rArr " "(dy_2)/(dx )=-((1)/(x))^(1//x)*(1)/(x^(2))(1+log ""(1)/(x))`