Hoe onderscheid je f (x) = (4x ^ 2 + 5) * e ^ (x ^ 2) met behulp van de productregel?

Antwoord:

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

Uitleg:

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

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

Laat # U = 4x ^ 2 + 5 # en # 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 + 4 x ^ 2 + 5) #

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