f(x)=(x^2+4)^2.(x+2)^3 f'(x) =…?

u=(x² + 4)² → u' = 2(x² + 4)
v = (x + 2)³ → v' = 3(x + 2)²
f'(x) = u'v + v'u
= 2(x² + 4)(x + 2)³ + 3(x + 2)(x² + 4)²
= (x + 2)²(x² + 4)(7x² + 8x + 12)
atau bntuk susunan lain

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

f(x) = (x² + 4)² (x + 2)³

f'(x) = 2 (x² + 4) (2x) (x + 2)³ + (x² + 4)² 3(x + 2)² (1)
       = 4x (x² + 4) (x + 2)³ + 3 (x + 2)² (x² + 4)²
       = 4x (x² + 4) (x + 2)³ {1 + 3 (x² + 4) / [4x (x + 2)]}
       = 4x (x² + 4) (x + 2)³ {[4x (x + 2) + 3 (x² + 4)] / [4x (x + 2)]}
       = (x² + 4) (x + 2)² [4x (x + 2) + 3 (x² + 4)]
       = (x + 2)² (x² + 4) (4x² + 8x + 3x² + 12)
       = (x + 2)² (x² + 4) (7x² + 8x + 12)