dq/dp simply means Change in quantity over Change in price. More specifically, How many units of quantity will be changed due to a price change.  And the units of change in quantity due to one unit change of price is the slope, which usually be expressed in equation as an index or proxy(e.g. Qdx=10-2Px , in this case, the slope, or dq/dp , is -2. Meaning one unit change of price x will lead to two units change of quantity of x.).
dQx / dPx * (Px/Qx) is the price elasticity of demand
dQx/ dPy * (Py/Qx) is the cross-price elasticity of demand
dQx/ dY  * (Y/Qx) is the income elasticity of demand

基本导数