Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Calculus - Differentiation - First Principles.
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The basic concept of differentiation that a secant becomes a tangent in its limiting position is outlined in this topic. The law of infinitisimals is a fundamental concept in much of mathematics especially in Calculus.

An understanding of the principles underlying differentiation is important to see where the techniques applied commonly are based.

The following table summarises, with the relevant links, the pages and videos relevant to learning about and evaluating your competency with the Product Rule.

Learning area. Resource.
Technique for Differentiating by First Principles with an example.
  First Principles - Test Yourself 1.
  First Principles - Test Yourself 1 Solutions.

For additional examples to practice with first principles, set yourself questions because you can use the short-cut method to see if you got it correct. Use Questions 1 or 2 and then both 3 and 4 as templates for your questions.