Yes, I tried defining it in as condescending a manner as possible. It is a term coming from Marxism, which is probably why it strikes you as being so stupid.
Well maybe you should have looked a little bit farther then your GOP hand book.
Productive wealth is wealth which is created. It is created by using productive resources, i.e. capital, labor and natural resources, to produce new, more and higher quantity and quality of goods and services.
Derived wealth is wealth which is not created, as in productive wealth, but wealth that is transferred, either from one individual to another or one group to another. Some examples, inheriting a fortune from your father is not productive wealth, it is derived, that is it was transferred. Winning the lottery is derived wealth. Gaming the market on mortgage derivatives is derived wealth. That is, it is a transfer of wealth from one individual or group to another, it is not productive wealth, that is, it is not wealth creation.
That can also be true of investing. If you invest money in a company with the idea that over time the company will improve it's productivity, create new products and services and thus produce wealth and the company is successfull in creating wealth and value of the stock rises and it pays you increased dividends as a result, then this is productive wealth.
If on the other hand you invest in a stock with the intent of buying it at a low price and selling to some sucker at a higher price and are succesfull at doing so, this is not productive wealth. It is a transfer of wealth from one person to another and is thus derived.
Another example would be real estate. If someone invests the capital to purchase the materials and labor to build a house and then sells that house at a price above the cost to create it, then this would be wealth creation. If on the other hand some one tries to buy an existing house at a low price and flip it at a higher price then they paid for it and is succesfull at doing so, then this is derived wealth. Wealth has not been created in this example but has been transferred.
Those who derive wealth are never, ever as valuable to our society as those who create wealth.