Let $f: \mathbb{C}^m \rightarrow \mathbb{P}^1$ be a function. The total derivative of $f$ denoted by $Df = \sum_{j=1}^{m}z_j \frac{\partial f}{\partial z_j}$. Moreover, $D^{k+1}f = D(D^kf)$. Let us consider the equation $\frac{D^{k+1}f}{D^{k}f-a} = \frac{D^{k+1}f}{D^{k}f}$. If we integrate the equation, then what do we get?
Is it like simple integration, and we get $D^{k+1}f -a = A(D^{k}f)$?
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