I have a weird representation for a discrete derivative problem. Say we have:
$$Δ M(x) = f(x) Δx$$
This means that we can rewrite it as $\frac{∂M(x)}{∂x} = f(x)$. However, the problem I face looks like this:
$$Δ M(x) = f(x) Δx + g(x) Δx^2$$
Thus, $$\frac{∂M(x)}{∂x} = f(x) + g(x) Δx$$
Can I also say that: $$\frac{∂^2M(x)}{∂x^2} = \frac{∂f(x)}{∂x} + g(x)$$
Or is this unacceptable? If not, then how do I get rid of the $Δx$ to move the problem from discrete to continuous?