- 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 :
Whenever possible, rewrite a function so it looks good before taking its derivative.
Any logarithm logb a can be written as
This allows us to find derivatives of logarithms in bases besides e.
We also know enough now to find derivatives of things like
f(x) = ln (x2).
We can bring down the exponent to find
f(x) = 2ln x,
and we know how to find the derivative of this:
Practice:
Example 1
Find the derivative of f(x) = log10 x. |
Example 2
Find the derivative of f(x) = log4 x2. |
Exercise 1
Find the derivative of the function.
- f(x) = log9 x
Exercise 2
Find the derivative of the function.
- g(x) = log2 x
Exercise 3
Find the derivative of the function.
- h(x) = ln x{10}
Exercise 4
Find the derivative of the function.
- j(x) = log4 x4
Exercise 5
Find the derivative of the function.
- k(x) = log5(x3)
