InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If `y=a^(x^(a^x..oo))` then prove that `dy/dx=(y^2 log y )/(x(1-y log x log y))` |
|
Answer» `y=a^(x^(a^x..oo))` `y-a^(x^(y)` `rArr log y =log x^(x^(y))` `x^(y).loga` `y-a^(x^(y)` `rArr log y =log x^(x^(y))` `x^(y).loga` `rArr log(log y)=log x^y+log(log a)` `=ylog x+log +log (log a)` Differentiate both sides with respect to x `1/(y log y )dy/dx=y/x+log x. dy/dx +0` `rArr (1/(y log y )-log x ) dy/dx = y/x ` `rArr ((1-y log x log y ) )/ (y log y ) .dy /dx = y/x` `dy/dx = (y^2 log y )/(x(1-y log x log y)` |
|