Question

Turunan pertama dari fungsi diatas adalah ......

#dilarang asal jawab, harus ada penyelesaian

Answer 1

→ turunan ←

y = u/v → y' = (u'v - uv')/v²

u = √x = x^1/2

u' = 1/(2√x)

v = 2x - 1

v' = 2

y' = (1/(2√x) . (2x - 1) - 2√x)/(2x - 1)²

atas bawah kalikan 2√x

y' = (2x - 1 - 4x)/(2√x . (2x - 1)²)

y' = (-2x - 1) / (2(2x - 1)² √x)

Answer 2

F(x) = √(x)/(2x-1)

F'(x) = (d(√(x)).(2x-1) - d(2x-1).√(x))/(2x-1)²

F'(x) = ((2x-1)/(2√(x)) - 2√(x))/(2x-1)²

      = ( (2x-1 - (2√(x))²/(2√(x)) )/(2x-1)²

      = (2x-1 - 4x)/(2√(x).(2x-1)²)

     = (-2x-1)/(2√(x).(2x-1)²)

F'(x) = -(2x+1)/(2√(x).(2x-1)²)