## About stationary and ws-stationary stochastical processes

Hi everyone.

I have started few days ago studying stochastical processes, and I'm trying to do and exercise that has me stuck.
Is the following:

$1\bullet$If $X(t)$ is a mean square differentiable wide-sense stationary stochastical process then the processes $X(t)$ and $X' (t)$ are orthogonal.

$2\bullet$If $X(t)$ is a twice mean square differentiable, stationary and Gaussian stochastical process, such that
$E[X(t)] = 0$, then $X(t)$ is independent of $X' (t)$ but not independent of
$X''(t)$

My teacher told me to use the formula: $\Gamma_{X^{(n)},X^{(m)}}(t,s)=(-1)^m\frac{d^{(n+m)}\Gamma_X(\tau)}{d\tau^{(n+m)}}$, where $\tau=t-s$, but it seems to get me nowhere...

Thanks a lot for any help.