If y= x x , then d^2 y d x^2 at x=1

Step-by-step solution

y= x x x y= x x d y d x +y= 1 x ...(i) d y d x = ( 1 x -y ) ( 1 x ) From Eq. (i), x d^2 y d x^2 + d y d x + d y d x =- 1 x^2 aligned & x d^2 y d x^2 +2 ( 1 x -y ) ( 1 x )=- 1 x^2 & At x=1,1 ( d^2 y d x^2 )+2 ( 1 1 - 1 1 ) ( 1 1 )=- 1 12 & d^2 y d x^2 =-3 aligned