Derivative of a Product
Provided the described limits exist, we've already discovered that
1) The derivative of a sum of two functions = the sum of the derivatives of these functions.
2) The derivative of a difference of two functions = the difference of the derivatives of these functions.
Yet what about replacing the word "sum" or "difference" with the word "product"?
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)?
Interact with the applet below for a minute. Study it carefully.
Move any 1 of the white points around if you need to.
Then answer the question in pink.