Question

Turunan pertama dari f(x)= (3x - 2)(4x + 1)^1/2 adalah f'(x). Nilai f'(2)?

Answer 1

Verified answer

TuRUNan

Misal :
u = 3x - 2 ---> u' = 3
v = (4x + 1)^1/2 ---> v' = 1/2 . 4(4x + 1)^-1/2
v' = 2/√(4x + 1)

f(x) = uv = (3x - 2)(4x + 1)^1/2

f'(x) = u'v + uv'
f'(x) = 3(4x + 1)^1/2 + (3x - 2) . 2/√(4x + 1)
f'(x) = 3√(4x + 1) + (6x - 4)/√(4x + 1)

f'(2) = 3√(4.2 + 1) + (6.2 - 4)/√(4.2 + 1)
f'(2) = 3.3 + 8/3
f'(2) = (9 × 3 + 8)/3
f'(2) = 35/3 = 11 2/3