Turunan dari y=(X²+12)(x+3)²

y = (x²+12)(x+3)²
y = (x²+12)((x)² + (2 x x x 3) + (3)²)
   = (x² + 12)(x² + 6x + 9)
   = x⁴ + 6x³ + 9x² + 12x² + 72x + 108
   = x⁴ + 6x³ + 21x² + 72x + 108

gunakan aturan perkalian
misal
[tex] u=x^{2} +12, u'=2x[/tex]
[tex] v=(x+3)^{2}, v'=2(x+3)[/tex]
jadi,
[tex] f'(x) =u'v+v'u[/tex]
[tex] f'(x) =2x (x+3)^{2} +(2x+6)(x^{2} +12)[/tex]
[tex] f'(x) =2x(x^{2} +6x+9)+2x^{3} +24x+6x^{2} +72)[/tex]
[tex] f'(x) =4x^{3}+18x^{2} +42x+72[/tex]