Say $N = ab$. How can I express $\frac{d}{dN}$ in terms of $\frac{d}{da}$ and $\frac{d}{db}$?
2026-03-25 06:26:04.1774419964
Question about differential operators
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Say we have a function $f=f(ab)$, then $$\frac{df}{dN}=\frac{df}{da}\cdot \frac{da}{dN}+\frac{df}{db}\cdot \frac{db}{dN} \\ =\frac{df}{da}\cdot \frac{1}{b}+\frac{df}{db}\cdot \frac{1}{a}$$ So $$\frac{d}{dN}=\frac{1}{b}\cdot \frac{d}{da}+\frac{1}{a} \cdot \frac{d}{db}$$