Hoe onderscheid je g (x) = (x ^ 2 + 1) (x ^ 2-3x) met behulp van de productregel?

Antwoord:

#G '(x) = 4x ^ 3-6x ^ 2 + 2x-2 #

Uitleg:

#G (x) = (x ^ 2 + 1) (x ^ 2-2x) #

Productregel:# D / dx (uv) = (du) / Dxv + u (dv) / dx #

# U = (x ^ 2 + 1) #

# Du / dx = 2x #

# V = x ^ 2-2x #

# Dv / dx = 2x = 2 #

# D / dx (x ^ 2 + 1) (x ^ 2-2x) = (du) / Dxv + u (du) / dx #

=# 2x (x ^ 2-2x) + (x ^ 2 + 1) (2 x-2) #

=# 2x ^ 3-4x ^ 2 + 2x ^ 3-2x ^ 2 + 2x-2 #

=# 4x ^ 3-6x ^ 2 + 2x-2 #