Question

Turunan y = x akar 2x adalah ...

Answer 1

1) y = (4x-3)(2x-1)^4
u = 4x-3 → u’ = 4
v = (2x-1)^4 → v’ = 4(2x-1)^3(2) = 8(2x-1)^3
y’ = u’v + v’u
= 4(2x-1)^4 + 8(2x-1)^3(4x-3)
= 4(2x-1)³((2x-1) + 2(4x-3))
= 4(2x-1)³(10x-7)

2) h(x) = √(3x - 2x²)
h’(x) = ½(3x – 2x²)^-½ (3 – 4x)
= ½(3 – 4x) / √(3x – 2x²) rasionalkan
= [(3 – 4x)√(3x – 2x²)] / 2x(3 – 2x)

3) y = (2/3) sin^5(2x)
y’ = 5(2/3) sin^4(2x) cos 2x
= (20/3) sin^4 (2x) cos (2x)