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:

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

$\displaystyle 2\bullet$If $\displaystyle X(t)$ is a twice mean square differentiable, stationary and Gaussian stochastical process, such that

$\displaystyle E[X(t)] = 0$, then $\displaystyle X(t)$ is independent of $\displaystyle X' (t)$ but not independent of

$\displaystyle X''(t)$

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

Thanks a lot for any help.(Nod)