Implicit differntiation using the chain rule

Could you explain how to find dy/dx for:
y = 2 sin ((pi*x) -y)

d/dx(y) = d/dx(2sin(pix - y))
dy/dx = 2cos(pix - y) (pi - dy/dx)
dy/dx = 2picos(pix - y) - 2cos(pix - y)dy/dx
dy/dx + 2cos(pix - y)dy/dx = 2picos(pix - y)
dy/dx(1 + 2cos(pix - y)) = 2picos(pix - y)
dy/dx = 2picos(pix - y)/(1 + 2cos(pix - y))

Chain rule is basically taking the derivative of the outside and multiplying it by the derivative of the inside and so on.
dy/dx [y=2sin(πx-y)]:
d/dx(y) = d/dx(2sin(πx-y))
dy/dx = 2cos(πx-y)*(π-dy/dx)
dy/dx = 2πcos(πx-y) - 2cos(πx-y)dy/dx
dy/dx + 2cos(πx-y)dy/dx = 2πcos(πx-y)
dy/dx(1 + 2cos(πx-y)) = 2πcos(πx-y)
dy/dx = 2πcos(πx-y) / (1+ 2cos(πx-y))