jika f(x) = x(x²+1) ³ maka f'' (x) =

Halo Ibrahim. Terima kasih sudah bertanya di Roboguru. Jawaban : f''(x) = 18x . (x²+1)² + 24x³ . (x²+1) Perhatikan penjelasan berikut ya. Ingat kembali: 1.) f(x) = u . v → f'(x) = u' . v + u . v' 2.) f(x) = a → f'(x) = 0 3.) f(x) = ax → f'(x) = a 4.) f(x) = axⁿ → f'(x) = a.n.xⁿ¯¹ 5.) f(x) = Uⁿ → f'(x) = n . Uⁿ¯¹ . U' Diketahui : f(x) = x . (x²+1)³ Ditanya : f''(x) = ... ? Maka: f(x) = x . (x²+1)³ u = x → u' = 1 v = (x²+1)³ → v' = 3 . (x²+1)² . 2x = 6x . (x²+1)² Diperoleh: f'(x) = u' . v + u . v' f'(x) = 1 . (x²+1)³ + x . 6x . (x²+1)² f'(x) = (x²+1)³ + 6x² . (x²+1)² f'(x) = (x²+1)³ + p . q p = 6x² → p' = 12x q = (x²+1)² → q' = 2 . (x²+1) . 2x = 4x . (x²+1) Sehingga: f'(x) = (x²+1)³ + p . q f''(x) = 6x . (x²+1)² + p' . q + p . q' f''(x) = 6x . (x²+1)² + 12x . (x²+1)² + 6x² . 4x . (x²+1) f''(x) = 18x . (x²+1)² + 24x³ . (x²+1) Jadi, f''(x) = 18x . (x²+1)² + 24x³ . (x²+1) Semoga membantu.