If y=e^ x x x , x>1 , then d^2 y d x^2 at x= _e 3 is

Step-by-step solution

Given, y=e^ x x x x , x>1 aligned & y=e^ x x x . . & _e y=( x x x . . ) )^ _e e & y= x x x . . y= x y & ( y)^2=x y ( y)^2 y =x & y=x & aligned Differentiating w.r.t. x , we get 1 y d y d x =1 d y d x =y Differentiating w.r.t. x , we get d^2 y d x^2 = d y d x d^2 y d x^2 =y [from Eq. (ii) ]...(iii) At x= _e 3 , from Eq (i), we get y= 3 y=3 Putting y=3 into Eq. (iii), we get d^2 y d x^2 =3