- 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 a
^{x} - 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

The chain rule patterns also help us to think backwards, which will be useful for something called "integration by substitution".

Example 1

What is a function whose derivative is 2 |

Exercise 1

Determine a function whose derivative is

- -3sin
*x*(cos*x*)^{2}

Exercise 2

Determine a function whose derivative is

- 6(
*x*^{3}+ 2*x*+ 1)^{5}(3*x*^{2}+ 2)

Exercise 3

Determine a function whose derivative is

- cos(
*x*+ 4)

Exercise 4

Determine a function whose derivative is

Exercise 5

Determine a function whose derivative is

- -6sin(6
*x*)