- 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

Finding derivatives of inverse trig functions will be similar to finding the derivative of *ln* x. Our main tool is the chain rule. We also need some background information:

- the fact that composing inverse functions gets us back where we started.

- the Pythagorean Theorem

- SOHCAHTOA

Example 1

Find the derivative of arcsin |

Exercise 1

Find the derivative of the function.

- arccos
*x*

Exercise 2

Find the derivative of the function.

- arctan
*x*