Jawaban:

To determine the first derivative of the function f (x) = (4x2−12x) (x + 2), we can work with two alternatives

First use the rule f (x) = u⋅v then f ′ (x) = u′⋅v + u⋅v ′

f(x) =(4x2−12x)(x+2)

u =4x2−12x→u′=8x−12

v = 4x2−12x→u′=8x−12

f′(x) =u′⋅v+u⋅v′ =(8x−12)(x+2)+(4x2−12x)(1) =8x2+16x−12x−24+4x2−12x =12x2−8x−24

Second, by simplifying the function to addition and subtraction.

f(x) =(4x2−12x)(x+2) =4x3+8x2−12x2−24x =4x3−4x2−24x

f′(x) =3⋅4x3−1−2⋅4x2−1−24 =12x2−8x−24