basic question about a W.S.S process

[serhannn]

If X(t) is a W.S.S process and its derivative is X'(t), how can we show that for a given t, Random Variables X(t) and X'(t) are orthogonal and uncorrelated?
I know that orthogonal means their correlation is zero and uncorrelated means their covariance is zero. Also using the constant-mean property of W.S.S processes I found that E[Y]=0, which leads to:
E[XY]=cov(X,Y)=corr(X,Y).
But how can I show that covariance and correlation are equal to zero.

Thanks a lot.

 

[lebesgue]

Do you think the random variables are independent?

 

[serhannn]

No, it is not stated in the question.