partial derivative

Given a cartesian coordinate system y_1, y_2, y_3
and another coordinate system (general one) x_1, x_2, x_3
while: y_1 = x_1 + 2x_2
y_2 = x_2 + 2x_3
y_3 = x_1 - 2x_2
find the distance element ds^2 in both coordinate systems.