How to solve $Cov(g(X),Y)$ when $(X,Y)$ has bivariate normal distribution

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I have a problem I cannot solve.

Suppose that $(X,Y)$ has the bivariate normal distribution. Prove that $$Cov(f(X),Y)=\frac{Cov(f(X),X)Cov(X,Y)}{Var(X)}$$