Derivatives

1) Average Rate of Change

2) Definition of a Derivative

3) Power Rule (and sum/difference, and constant multiple rules)

4) Product & Quotient Rule

• Explanation:

• Practice Problems:

6) Product and Quotient Rule with Symbolic Notation

• Explanation:

• Practice Problems

7) Derivative of Trig Ratios

• Explanation:

• Practice Problems:

8) Chain Rule

• Explanation:

• Practice Problems:

• Explanation

• Practice Problems

10) Derivative of Exponential & Logarithmic Expressions

11) Use differentiation rules when given the definition of a derivative

12) Derivative Rules using tables and graphs

• Practice Problems

13) Review Summary:

• The Chain Rule. The last operator is what you keep; all of the other operators are "u."

• When should you use the chain rule:

• When you have a power (numerical exponent) and the base is anything other than a single variable.

• When you have a trig ratio and the "inside" part is anything other than a single variable

• When you have an exponential function (the base is a number) and the exponent is anything other than a single variable.

• When you have a logarithmic function and the "inside" part is anything other than a single variable.

14) Derivative at a point with a calculator

15) Implicit differentiation - one dy/dx

• Explanation:

• Practice Problems:

16) Implicit differentiation - more than one dy/dx

• Explanation

• Practice Problems

17) Review Implicit Differentiation

18) Derivative of Inverse Functions

• Explanation:

• Practice Problems:

19) Derivative of Inverse Functions with the graphing calculators

20) Derivative of Inverse Trig Ratios

• Explanation:

• Practice Problems:

21) Points of Non-Differentiability

• Explanation:

• Practice Problems:

22) Review

23) Derivative Cumulative