Derivatives

delta x in the denominator cancels out delta x in the numerator. In order to obtain a derivative using its definition, you must simplify the numerator to the point where it's just a number * delta x, allowing the delta x in the denominator to be cancelled out. Think of it as simplifying a fraction: for example, in order for 2/6 to be simplified, one must divide by the LCM (2). In the case of the definition of a derivative, the LCM is delta x.