Provided the described limits exist, we've already discovered that [br][br]1) The derivative of a sum of two functions = the sum of the derivatives of these functions. [br]2) The derivative of a difference of two functions = the difference of the derivatives of these functions.[br][br]Yet what about replacing the word "sum" or "difference" with the word "product"? [br][color=#ff00ff][b]That is, is the derivative of the product of two functions evaluated at any input = the product of the derivatives of these two functions (evaluated at this same input)? [/b][/color][br][br]Interact with the applet below for a minute. Study it carefully. [br]Move any 1 of the white points around if you need to. [br][br][color=#ff00ff][b]Then answer the question in pink.[/b][/color]