math120 ch25g2 combining derivative rules
Realistic problems often need a combination of derivative rules, like product rule and chain rule and constant-multiplier rule, etc. In this video we try to show every step; in the next video we take a streamlined approach. It's fine to do whichever works for you.
Spotting the individual parts of a formula, and how they each work and go together, is an example of the Mathematical Practice "Look for and make use of structure"..."see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects." It's good for future teachers especially to think about the value of being able to see structure in algebraic expressions.