- 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've seen lines before. The restroom at half-time, the blue things on notebook paper...and they were all over algebra. y = mx + b, anyone? Lines are a special case of polynomials. Once we master them, we'll be ready to add some power. As in the power of 2. Not rangers.
Practice:
Example 1
Let f(x) = 4x + 2. What is f'(x)? |
Exercise 1
Find the derivative of the function f(x) = 3x + 5.
Exercise 2
Find the derivative of the function f(x) = 2x.
Exercise 3
Find the derivative of the function f(x) where f is the line that passes through the points (4,5) and (-1,-2).
.Exercise 4
Find the derivative of the function f(x) = 4.
Exercise 5
Find the derivative of the function f(x) = 7(x - 1) + 3.
