Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Calculus I
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^xand 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

Supplemental Resources (optional)

rev. 2020-10-10