Aplicando las reglas de la derivación calcular las siguientes derivadas.

1. f ( x )=x+ ln (x)

f ' ( x )= (x )'+(lnx) '

f ( x )=1+ 1xó f ' (x )= x+1

x

2. f ( x )=ex−√ x−2

f ( x )=ex−( x )12−2

f ' ( x )=(ex )'−[ x 12 ]'

−(2)'

f ' ( x )=ex−12x

−12 −0

f ' ( x )=e x− 12√ x

3. f ( x )=x . ex

f ' ( x )=( x )' . ex+x (ex )'

f ' ( x )=1.ex+xe x

f ' ( x )=e x(1+x )

4. f ( x )=x2 . ln (x )

f ' ( x )=(x2 )' . ln ( x )+x2 .(lnx) '

f ' ( x )=2 x . ln ( x )+x2 . 1x

f ' ( x )=2 x . ln ( x )+x

5. f ( x )= x4

ex

f ' ( x )= (x4 )' . ex−x4 . (ex )'

(e x)2

f ' ( x )=4 x3 ex−x4 ex

(ex)2f ' ( x )= e

x (4 x3−x4)e2 x

f ' ( x )=4 x3−x4

e x