Vraag # e2a9c

Antwoord:

# "Zie uitleg" #

Uitleg:

#f '(x) = lim_ {h-> 0} (f (x + h) - f (x)) / h #

#"Hier hebben we"#

#f (x) = ln (x) #

# => f '(x) = lim_ {h-> 0} (ln (x + h) - ln (x)) / h #

# = lim_ {h-> 0} ln ((x + h) / x) / h #

# = lim_ {h-> 0} ln (1 + h / x) / h #

# = y #

# => e ^ y = lim_ {h-> 0} (1 + h / x) ^ (1 / h) #

# = e ^ (1 / x) "(Euler-limiet)" #

# => y = 1 / x #

# => f '(x) = 1 / x #