what does it mean to derive an equation
One is taking the derivative of an equation. That means to find out the rate at which one quantity changes as a function of the other quantity. For example, if we know the equation that describes the level of water in a swimming pool at any given time, we can figure out the rate that that water changes over time by taking the derivative. The other term is to derive an equation. This means to take a first-principles approach to figure an equation that describes some phenomena. For example, knowing that mass and energy are conserved, and with the assumption of incompressibility, we can derive the equation that will describe an ideal fluid's motion through a pump.