Turunan fungsi f(x) = (x + 7)(x – 5x + 3)

Turunan Fungsi

f(x) = (x + 7)(x² – 5x + 3)

Andaikan

f(x) = U(x).V(x)

dimana

U(x) = (x + 7)

V(x) = (x² – 5x + 3)

Maka, gunakan rumus turunan fungsi f(x)

f'(x) = U'(x).V(x) + U(x).V'(x)

Mencari U'(x)

U(x) = x + 7   <— Gunakan rumus turunan axⁿ = a.n xⁿ⁻¹

U'(x) = [ 1(1)x¹⁻¹ ] + [ 7(0)x⁰⁻¹ ]

U'(x) = 1 + 0

U'(x) = 1

Mencari V'(x)

V(x) = x² – 5x + 3 <—- Gunakan rumus turunan axⁿ = a.n xⁿ⁻¹

V'(x) = [ 1(2)x²⁻¹ ] – [ 5(1)x¹⁻¹ ] + [ 3(0)x⁰⁻¹ ]

V'(x) = 2x – 5

Masukkan ke rumus turunan fungsi f(x)

f(x) = U(x).V(x)

f'(x) = U'(x).V(x) + U(x).V'(x)

f'(x) = 1(x² – 5x + 3) + (x + 7)(2x – 5)

f'(x) = (x² – 5x + 3) + (2x² + 9x – 35)

f'(x) = x² + 2x² – 5x + 9x + 3 – 35

f'(x) = 3x²+4x−32

Jadi, Turunan fungsi f(x) = (x + 7)(x² – 5x + 3), adalah f'(x) = 3x²+4x−32

Sehingga, gunakanlah pilihan C. 3x² + 4x – 32

Semoga membantu 🙂