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.
Quotients are harder.
This is called the Chain Rule. Higher Derivatives You can take a derivative of a derivative. That second derivative is called, well, a second derivative. Third and higher derivatives are similarly defined. If the second derivative is zero, the curve is switching from one curvature to the other and is at an inflection point .