If f(x)= _ x^2 ( x) , then f^ (x) at x=e is

Step-by-step solution

f(x)= _ x^2 ( x) f^ (x)= d d x _ x^2 ( x)= d d x ( x) (x^2 ) [ d d x u v = v u^ -u v^ v^2 , d d x x= 1 x . and . _a b= _e b _e a ] aligned & = d d x ( x) 2 x & = 1 2 x 1 x 1 x - ( x) 1 x ( x)^2 & = 1 2 [ 1 x (1- ( x) ( x)^2 ] aligned aligned & At, x=e & f^ (e)= 1 2 e ( _e e )^2 (1- _e ( _e e ) ) & f^ (e)= 1 2 e (1)^2 (1-0)= 1 2 e =(2 e)⁻¹ aligned