Supose $f,g$ and $h$ are in $C^n(\mathbb{R})$ such that $$f^{(n)}=\sum_{k=0}^ng^{(k)}h^{(n-k)}.$$
Is there a simple way to obtain $f$ in terms of $g$ and $h$ such that $f$ does not depend on the derivatives?
I try with Leibniz derivation product rule, but the binomial coefficients implies to many problems.