If f(x)= _ x² ( x) , then f^ (x) at x=e is

Step-by-step solution

We have, f(x)= _ x² ( x) f(x)= 1 2 [ _ x ( x) ] [ _ a^ n b= 1 n _ a b ] f(x)= 1 2 [ ( x) x ] ( _ a b= b a ) f^ (x)= 1 2 [ (x) d d x [ ( (x))]- ( x) d d x x ( x)² ]= 1 2 [ (x) 1 x 1 x - ( ( x) 1 x ) ( x)² ]= 1 2 [ 1 x - ( (x)) x ( x)² ] f^ (x)= 1 2 [ 1- (x) x( x)² ] f^ (e)= 1 2 [ 1- (e) e( e)² ]= 1 2 [ 1-0 e ]= 1 2 e