Diketahui fungsi g(x) = (3x + 2)(5 – 2x)². Turunan pertama fungsi g(x)

adalah

36x² – 104x + 35

Penyelesaian:

g(x) = (3x + 2)(5 – 2x)²

Misal:

u(x) = 3x + 2

➔ u'(x) = 3

v(x) = (5 – 2x)²

➔ v'(x) = 2(5 – 2x)¹ × –2 = 10 – 4x × (–2) = –20 + 8x

Gunakan rumus turunan fungsi

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

g'(x) = 3 × (5 – 2x)² + (3x + 2)( –20 + 8x)

= 3 (25 – 20x + 4x²) – 60x + 24x² – 40 + 16x

= 75 – 60x + 12x² – 44x + 24x² – 40

= 36x² – 104x + 35