Question

Tentukan nilai f'(x) jika f(x) = 3x - 1 / 1 + 2x​

Answer 1

Turunan fungsi untuk f(x) = u/v ----> f'(x) = u'v - v'u/v²

f(x) = 3x - 1/1 + 2x

• u = 3x - 1 ---> u' = 3
• v = 1 + 2x ----> v' = 2

maka:

f'(x) = 3(1 + 2x) - 2(3x - 1)/(1 + 2x)²

f'(x) = 3 + 6x - 6x + 2/(1 + 2x)²

f'(x) = 5/(1 + 2x)²

Answer 2

PENJELASAN:

f(x)=(3x-1)/(1+2x)

u = 3x - 1

u' = 3

v = 1 + 2x

v' = 2

f'(x) = (u'.v - u.v')/(v^2)

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

f'(x) = (3 + 6x - 6x + 2)/((1+2x)^2)

f'(x) = 5/((1+2x)^2)

f'(x) = 5/(4x^2 + 4x + 1)

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Jawaban: f'(x) = 5/(4x^2 + 4x + 1).