Suppose we have an arbitrary function of two variables: $f(x,y)$. The question I ask would be for any functional form of this function, as long as it depends on $x$ and $y$.
We know that $\frac{df}{dy} > 0$, and $\frac{df}{dx} > 0$, does this information suffice to assert that:
$$\frac{d}{dx} (\frac{df}{dy}) > 0?$$