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Calculus I: Differentiation, Applications, and Optimization Study Guide

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Basic Rules of Differentiation

  • The Power Rule: Negative & Rational Exponents
    04:09
  • The Power Rule: Negative & Rational Exponents Example 1
    03:37
  • The Power Rule
    04:02

Derivatives of Exponential & Logarithmic Functions

  • Derivatives of General Logarithmic Functions
    06:32
  • Derivative of the Natural Logarithmic Function
    05:18
  • Derivative of the Natural Exponential Function (e^x) Example 3
    02:38

Derivatives of Inverse Trigonometric Functions

  • Derivatives of Other Inverse Trigonometric Functions
    06:35
  • Derivatives of Inverse Sine & Inverse Cosine Example 1
    03:36
  • Derivatives of Inverse Sine & Inverse Cosine
    07:26

The First Derivative Test

  • The First Derivative Test: Finding Local Extrema Example 3
    11:22
  • The First Derivative Test: Finding Local Extrema Example 2
    04:00
  • The First Derivative Test: Finding Local Extrema Example 4
    05:00

Concavity

  • Determining Concavity Given a Function Example 3
    02:33
  • Determining Concavity from the Graph of f' or f''
    03:56
  • Determining Concavity Given A Function Example 2
    6:08

The Second Derivative Test

  • The Second Derivative Test: Finding Local Extrema
    06:02
  • The Second Derivative Test: Finding Local Extrema Example 1
    05:34

Intro to Extrema

  • Finding Extrema Graphically Example 1
    04:45
  • Finding Extrema Graphically Example 2
    02:46
  • Finding Extrema Graphically
    05:58

Applied Optimization

  • Intro to Applied Optimization: Maximizing Area
    10:13
  • Example 5: Packaging Design
    08:29
  • Example 4: Norman Window
    13:49

Linearization

  • Percorso guidato
    Linearization
    07:17

Introduction to Limits

  • Cases Where Limits Do Not Exist Example 2
    03:33
  • Finding Limits Numerically and Graphically
    6:47
  • Cases Where Limits Do Not Exist
    03:07