What Basic Derivative Rule Is Responsible For This?

If:

$$a(x)=b(x)-c(x)$$

Then:

$$\frac{da}{dx}=\frac{db}{dx}-\frac{dc}{dx}$$

Please note that the sum/difference rule is not directly invoked since it talks about a derivative of a sum/difference being equal to the sum/difference of the derivatives. It could very well be the basis for this logic, although I don't see it offhand. And of course, this is not a homework question. I came across this logic today and was surprised I could use it.

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