Calculus – Unit 4 – Applications of Derivatives

Three (maybe four) major ideas dominate this unit:

  1. The Chain Rule as a concept is essential to extending calculus to context based situations.
  2. Implicit Differentiation is an application of the Chain Rule that allows us to solve problems that would otherwise be impossible to solve.
  3. Related Rates help us understand how more than one quantity are intertwined with one another and we need to use both the chain rule and implicit differentiation to uncover new ideas.
  4. (bonus) Also, organization of information and notation are more important than ever!

In an effort to support the learning that is happening in class, these three videos will provide the conceptual understanding behind these Calculus ideas and also provides several examples of how to use them in our course, this is procedural fluency which is just as important as concept understanding.

The Chain Rule

Work to understand how the notation of d/dx is similar to dy/dx. Along with an understanding of fractions, this is a key idea in Calculus.

Implicit Differentiation

Think about how the Chain Rule is being applied to each situation.

Related Rates

When solving these problems, they get easier the more you work to understand them. STAY ORGANIZED!