The sign error calculating the derivative of a contravariant metric with respect to the covariant metric as diff(g_[`~nu`, `~tau`], g_[mu, eta]) and vice versa based on the Physics package is meanwhile resolved if you install the lastes update version 315.

However, a similar error occurs with the Tetrad package. If one calculates

diff(e_[~a, mu], e_[b, ~nu])

the obtained result is

eta_[~a, ~b] * g_[mu, nu].

But the is wrong! The correct result is

-e_[~a,nu] * e_[~b,mu].

When I try to calculate the derivative of a covariant metric with respect to the corresponding contravariant metric, or vice versa, the result is correct up to the sign, which is wrong:

diff(g_[nu, tau], g_[~mu, ~eta]);

Maple's result: g_[eta, nu] g_[mu, tau]

Correct result: -g_[eta, nu] g_[mu, tau]

diff(g_[~nu, ~tau], g_[mu, eta]);

Maple's result: g_[~eta, ~nu] g_[~mu, ~tau]

Correct result: -g_[~eta, ~nu] g_[~mu, ~tau]

I've loaded DifferentialGeometry, Tensor, Physics. Is this my fault, or Maple's?