Note : I mainly consider the case in which demand curves are linear , to keep things simple.
I'm having trouble in applying mathematics to (micro)economics due to the fact that in this discipline , the independent variable is standardly placed on the Y axis (while it is placed on the x axis in mathematics).
In economics, we are presented with demand curves.
My question deals with the meaning of the "slope" of such curves.
A demand curve is supposed to represent a demand function (with price as independent variable, on the Y axis) $ D = f(P)$.
The "gradient" of this function is given by $ \frac {\Delta D} {\Delta P}$ (or its limit in the non-linear case). .
But when we calculate the slope of the demand function we do it "the ordinary ( mathematical ) way", that is we calculate the ratio "rise over run" : $ \frac {\Delta P} {\Delta D}$.
So is it correct to say that , in fact, the slope of the demand curve ( or of its tangent in case the curve is not linear) is not the gradient of the demand function, but in fact, the inverse of the gradient of the demand function?
Example : Let the demand function be $D(p) = -2p+10$ . The gradient of this function is $-2 = -2/1$ but the slope of the demand curve is $1/-2 = - 1/2$.