Let $X$, $Y$, and $Z$ be continuous random variables. $X$ and $Y$ are independent with respect to each other, while $Z = g(X, Y)$.
$E(X)$, $E(Y)$, and $E(Z)$ are known. Marginal pdf's $f_X(x)$, $f_Y(y)$, and $f_Z(z)$ are known. Joint pdf's not given.
I am attempting to compute the covariance $Cov(Z, X)$. I know that $$ Cov(Z, X) = E(ZX) - E(Z)E(X) $$ but I am unsure how to compute $E(ZX)$ with $Z$ dependent on $X\ \ $ ($Z = g(X, Y)$).
What is the approach to evaluating the covariance of two dependent random variables?