turunan y = ((2x²-5))³+5)-2

Turunan Berantai Fungsi Aljabar.
Matematika wajib kelas XI kurikulum 2013 revisi 2016.

y = [(2x² - 5)³ + 5]⁵ - 2

y' = 5 [(2x² - 5)³ + 5]⁴ [3(2x² - 5)² (4x) + 0]- 0
    = 60x [(2x² - 5)³ + 5]⁴ (2x² - 5)²
Jawaban: B.

y = ((2x^2 - 5)^3 + 5)^5 - 2
Misal
u = 2x^2 - 5
=> du/dx = 4x

v = (2x^2 - 5)^3 + 5
v = u^3 + 5
=> dv/du = 3u^2
=> dv/du = 3(2x^2 - 5)^2

y = ((2x^2 - 5)^3 + 5)^5 - 2
y = v^5 - 2
=> dy/dv = 5v^4
=> dy/dv = 5((2x^2 - 5)^3 + 5)^4

y' = dy/dx
= dy/dv . dv/du . du/dx
= 5((2x^2 - 5)^3 + 5)^4 . 3(2x^2 - 5)^2 . 4x
= 5 . 3 . 4x . ((2x^2 - 5)^3 + 5)^4 . (2x^2 - 5)^2
= 60x ((2x^2 - 5)^3 + 5)^4 . (2x^2 - 5)^2