So the derivative of a constant is zero. So the derivative of a constant times a function is the constant times the derivative of the function. We can apply the approximation method to other functions as well. The exponential function is its own derivative. Well, yes it is, once you eliminate the formal junk that clutters the average calculus text and get down to finding results.
Formal mathematics is important.
So is fixing jet engines, but you don't need to be a trained aviation mechanic to fly a plane. There are two ways of writing derivatives. The other notation treats derivatives as a function. This is just the sum of the two derivatives. It's easy to see that subtraction works the same way.