Topic: Derivatives

Subtopic: Derivatives of Basic Functions

**Overview**

Now that we know how to find a derivative using the formal definition, let's look for an easier way! Today we learn to find derivatives of basic functions such as using the power rule to find the derivative of a polynomial function.

**Objectives**

By the end of this topic you should know and be prepared to be tested on:

- 2.2.1 Use correct mathematical notation when writing a derivative (including Newton and Leibniz notation)
- 2.2.2 Apply the power rule to expressions of the form `kx^p` where `p` is any Real number
- 2.2.3 Know that the derivative of a constant is zero and be able to explain why both algebraically and graphically
- 2.2.4 Apply basic derivative rules including the constant multiple rule, the sum rule, and the difference rule
- 2.2.5 Apply the power rule to find the derivative of a polynomial function
- 2.2.6 Find slope and equation of tangent line to a basic function using the derivative without using the formal definition of derivative
- 2.2.7 Know the derivative of `sinx`, `cosx`, and `e^x`
- 2.2.8 Use correct mathematical notation when writing a higher order derivative including Newton and Leibniz notation
- 2.2.9 Find higher order derivatives of basic functions including power, polynomial, `sinx`, `cosx`, and `e^x`

**Terminology**

Terms you should be able to define: Newton notation, Leibniz notation, power rule, constant rule, constant multiple rule, sum rule, difference rule, higher-order derivative

**Text Notes**

- Some text present material in an untraditional order. Personally I find it useful to learn the derivative of `e^x`and how to find higher-order derivative (second derivatives, third derivatives, etc.) early on even if we won't formally test on all of these topics immediately.
- At some point your text will start using two different notations one developed by Isaac Newton and the other developed coincidedly by Gottfried Wilhelm Leibniz. Be sure that you are able to correctly use either notation for first and higher-order derivatives.

**Mini-Lectures and Examples**

STUDY: Derivatives of Basic Functions

**Supplemental Resources (optional)**

Video: Differentiation Formulas, Selwyn Hollis's Video Calculus

and Higher Order Derivatives, Selwyn Hollis's Video Calculus

rev. 2020-10-10