Ableiten mit Produktregel: (x - 2) * (x^2 - 4x - 12)

Question

(x-2)* (x^2-4x-12)

wie lautet die 1. Ableitung

danke schön.

Answer 1

f(x) = (x - 2) * (x² - 4x - 12)

u = (x - 2)
u' = 1

v = (x^2 - 4x - 12)
v' = (2x - 4)

(u * v)' = u' * v + u * v'

f'(x) = 1 * (x^2 - 4x - 12) + (x - 2) * (2x - 4)
f'(x) = x^2 - 4x - 12 + 2x^2 - 8x + 8
f'(x) = 3x^2 - 12x - 4