Using implicit differentiation, find the derivative of (dy)/(dx) for the equation √(xy)=2+x²y³. Choose the correct option below:

A) (dy)/(dx) = (2 + x²y³)/(2√(xy))
B) (dy)/(dx) = (2 + x²y³)/(2xy)
C) (dy)/(dx) = (2 + x²y³)/(2x√(y))
D) (dy)/(dx) = (2 + x²y³)/(2y√(x))