# Economic Elasticity: where elasticity-equation come from?

I know the equation for economic elasticity is:

$$\varepsilon = \frac{\%\,\Delta Y}{\%\,\Delta X}\frac{X}{Y} = \frac{\partial Y(X)}{\partial X}\frac{X}{Y} = \frac{\partial \log(Y)}{\partial \log(X)}$$

In fact, this is the generalization for any sensitive-analysis or elasticity for a given function; in this case $Y(X)$.

But, where does come it from? I mean, why is it the equation and no -for example- just the partial derivate of the given function?