Wie unterscheidet man f (x) = (4x ^ 2 + 5) * e ^ (x ^ 2) anhand der Produktregel?

Antworten:

#f '(x) = 2xe ^ (x ^ 2) (4x ^ 2 + 9) #

Erläuterung:

Produktregel: #f '(x) = u'v + v'u #

#f (x) = (4x ^ 2 + 5) * e ^ (x ^ 2) #

Lassen # u = 4x ^ 2 + 5 # und # v = e ^ (x ^ 2) #

# u '= 8x #

# v '= 2xe ^ (x ^ 2) #

#:. f '(x) = 8x * e ^ (x ^ 2) + 2xe ^ (x ^ 2) * (4x ^ 2 + 5) #

# = 2xe ^ (x ^ 2) (4 + 4x ^ 2 + 5) #

# = 2xe ^ (x ^ 2) (4x ^ 2 + 9) #