- Topics At a Glance
- Derivatives of Basic Functions
- Constant Functions
- Lines
- Power Functions
- Exponential Functions
- Logarithmic Functions
- Trigonometric Functions
- Derivatives of More Complicated Functions
- Derivative of a Constant Multiple of a Function
- Multiplication by -1
- Fractions With a Constant Denominator
- More Derivatives of Logarithms
- Derivative of a Sum (or Difference) of Functions
- Derivative of a Product of Functions
- Derivative of a Quotient of Functions
- Derivatives of Those Other Trig Functions
- Solving Derivatives
- Using the Correct Rule(s)
- Giving the Correct Answers
- Derivatives of Even More Complicated Functions
- The Chain Rule
- Re-Constructing the Quotient Rule
- Derivative of ax
- Derivative of ln x
- Derivatives of Inverse Trigonometric Functions
- The Chain Rule in Leibniz Notation
- Patterns
- Thinking Backwards
- Implicit Differentiation
- Computing Derivatives Using Implicit Differentiation
- Using Leibniz Notation
- Using Lagrange Notation
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem
Introduction to :
We found the derivatives of sin and cos, and now that we have the quotient rule we can take derivatives of all those other trig functions we didn't discuss yet.
We used three general steps in the above problem.
- We rewrote the function in terms of sin and cos,
- we used the quotient rule, and
- we wrote the answer in terms of trig functions.
Practice:
Example 1
Find the derivative of tan x. |
Exercise 1
Find the derivative of each function.
- csc x
Exercise 2
Find the derivative of each function.
- sec x
Exercise 3
Find the derivative of each function.
- cot x
