I think you are thoroughly misunderstanding the notation. When we write dQ/dP, it is not a division; it just means the derivative of Q

__with respect to__ P. You should think of it as a single symbol. Other books might avoid this notation and call it Q' instead.

dQ is not the derivative of Q; it is called a "differential", and is not needed here.

So if Q = 60 - 3P, then we say that dQ/dP = -3, not that dQ = -3. (Note also that we take the derivative of a

*function*, not of an

*equation*, and you must always state

*with respect to* what.)

Furthermore, you must take a derivative before assigning a specific value to any variable, because once you assign a value, nothing is varying any more, and derivatives are all about how something varies. So if P were a function of something and you took the derivative "when P = 15", you would not take the derivative of the function P = 15, which is 0; you would find the derivative of that function, and

*then *replace P with 15.

But here P is the independent variable; it is not a function of anything, so you don't take its derivative. You take the derivative of Q with respect to P.

So, yes, this is a silly question; has it been a long time since you took calculus, or have you not yet really studied it, and are trying to understand the economics with no real knowledge of what derivatives are? We might have suggestions for what you need to study.

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