Turunan pertama f(x) = (x²-5x)³ adalah f'(x) =....... A. (x²-5x)²(6x-15) B. (X²-5x)²(2x-5) C. (x²-5x) (6x-15) D. 3(x²-5x)² E. 3(x²-5x) Beserta cara pengerjaan

Jika :
f(x) = (g(x))^n
maka
f'(x) = n . (g(x))^(n-1) . g'(x)

n = 3
g(x) = x^2 - 5x
g'(x)
= 2 . x^(2-1) - 5 . 1. x^(1-1)
= 2x - 5

f'(x)
= 3 . ( (x^2 - 5x)^2) . (2x - 5)
= (x^2 - 5x)^2 (6x - 15)

A

Turunan Fungsi Aljabar.
Kelompok wajib kelas XI kurikulum 2013 revisi 2016.

f(x) = [u(x)]ⁿ → f'(x) = n [u(x)]ⁿ⁻¹ u'(x)

f(x) = (x² - 5x)³
f'(x) = 3(x² - 5x)² (2x - 5)
       = (x² - 5x)² (6x - 15)