Tentukan turunan pertama dari f(x) = (2x+4) (3x²-3)²

Penyelesaian:

misal:

u = 2x+4

u' = 2

.

v = (3x²-3)²

v' = 2(3x²-3)(6x)

v' = 12x(3x²-3)

.

f(x) = uv

f'(x) = u'v + v'u

f'(x) = 2(3x²-3)² + 12x(3x²-3)(2x+4)

f'(x) = 2(3x²-3)((3x²-3)+6x(2x+4))

f'(x) = 2(3x²-3)(3x²-3+12x²+24x)

f'(x) = 2(3x²-3)(15x²+24x-3)

f'(x) = 6(3x²-3)(5x²+8x-1)