f ( x ) = ( 1 + ln ( x ) ) / x
u = 1 + ln ( x )
u ´= 1 / x
v = x
v ´ = 1
Quotientenregel
f ´( x ) = [ ( 1/ x * x ) - ( 1 + ln ( x ) ) * 1 ) ] / x^2
f ´( x ) = [ 1 - 1 - ln ( x ) ] / x^2
f ´( x ) = - ln ( x ) / x^2
1.Ableitung 0
- ln ( x ) / x^2 = 0
- ln ( x ) = = 0
x = 1
f ´´ ( x ) = [ 2 * ln ( x ) - 1 ] / x^3
[ 2 * ln ( x ) - 1 ] / x^3 = 0
2 * ln ( x ) - 1 = 0
ln ( x ) = 1 / 2
x = e^{1/2}