3.5 Selecting Procedures for Calculating Derivatives

By this point in the course, you know multiple derivative rules: the power rule, constant and sum rules, trig derivatives, exponential and logarithmic derivatives, the product rule, the quotient rule, and the chain rule. The challenge now is not just doing derivatives, but deciding which rule or combination of rules to use. This lesson is about recognizing structure. If an expression is a sum, differentiate term by term. If it is a product of two nontrivial functions, use the product rule. If it is a quotient of two nontrivial functions, use the quotient rule. If one function is nested inside another, use the chain rule. If more than one of these patterns appears at once, then multiple rules may be needed in the same problem.