Implicit Differentiation – In this section we will discuss implicit differentiation. Not every function can be explicitly written in terms of the independent variable, e.g. y = f(x) and yet we will still need to know what f'(x) is. Implicit differentiation will allow us to find the derivative in these cases. Knowing implicit differentiation will allow us to do one of the more important applications of derivatives, Related Rates (the next section).
Related Rates – In this section we will discuss the only application of derivatives in this section, Related Rates. In related rates problems we are give the rate of change of one quantity in a problem and asked to determine the rate of one (or more) quantities in the problem. This is often one of the more difficult sections for students. We work quite a few problems in this section so hopefully by the end of this section you will get a decent understanding on how these problems work.
Higher Order Derivatives – In this section we define the concept of higher order derivatives and give a quick application of the second order derivative and show how implicit differentiation works for higher order derivatives.
3.7B – More Implicit Differentiation
3.8 – Higher- Order of Derivatives (Velocity &Acceleration)
3.9 A– Derivate of Exponential Functions
3.9 B– Derivates of Exponential and Logarithmic Functions
3.10 A– Related Rates – Part 1
3.10 B – Related Rates – Part 2
3.10 C – Related Rates – Part 3
3.11 – Derivatives of Other Trigonometric Functions
3.13 Chapter 3 Review – Implicit Diff. and Related Rates