### 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.