Differential Calculus

Learning tasks

A) Derivative
I) Rate of Change
1) Finding Rate of Change	Ex 1 Ex 2 Ex 3 Ex 4
2) Finding Rate of Change from a Graph	Ex 5 Ex 6 Ex 7 Ex 8
3) Modeling with Rates of Change	Ex 9 Ex 10 Ex 11 Ex 12
4) Modeling with Rates of Change	Ex 13 Ex 14 Ex 15
II) Limit Definition of the Derivative
5) Conjecturing the Derivative at a Point	Ex 16 Ex 17 Ex 18
6) Finding the Derivative Graphically	Ex 19 Ex 20 Ex 21 Ex 22
III) Derivative Function
7) Finding the Derivative from First Principles	Ex 23 Ex 24 Ex 25 Ex 26 Ex 27
8) Interpreting the Graph of the Derivative	Ex 28 Ex 29 Ex 30
9) Finding the Tangent Slope Using the Derivative Function	Ex 31 Ex 32 Ex 33
IV) Conditions of Differentiability
10) Identifying Differentiability from a Graph	Ex 34 Ex 35 Ex 36
B) Rules of Differentiation
I) Basic Rules and Power Functions
11) Proving Basic Rules and Power Functions	Ex 37 Ex 38 Ex 39 Ex 40
12) Applying the Power Rule	Ex 41 Ex 42 Ex 43 Ex 44 Ex 45
13) Differentiating Polynomial Functions	Ex 46 Ex 47 Ex 48 Ex 49
14) Differentiating Functions with Fractional and Negative Exponents	Ex 50 Ex 51 Ex 52 Ex 53
15) Expanding Before Differentiating	Ex 54 Ex 55 Ex 56 Ex 57
II) Chain Rule
16) Forming Composite Functions	Ex 58 Definition Polygon A polygon is a flat, closed shape made of straight sides that do not cross each other. Ex 59 Ex 60
17) Decomposing Composite Functions	Ex 61 Ex 62 Ex 63 Ex 64
18) Differentiating with the Chain Rule	Ex 65 Definition Polygon A polygon is a flat, closed shape made of straight sides that do not cross each other. Ex 66 Ex 67
III) Product Rule
19) Differentiating with the Product Rule	Ex 68 Ex 69 Ex 70 Ex 71
IV) Quotient Rule
20) Differentiating with the Quotient Rule	Ex 72 Ex 73 Ex 74 Ex 75
V) Implicit Differentiation
21) Finding the Derivative of an Implicit Function	Ex 76 Ex 77 Ex 78
22) Finding the Slope of a Tangent Line of an Implicit Function	Ex 79 Ex 80 Ex 81
C) Derivatives of Standard Functions
I) Exponential Functions
23) Differentiating Exponential Functions: Level 1	Ex 82 Ex 83 Ex 84 Ex 85
24) Differentiating Exponential Functions: Level 2	Ex 86 Ex 87 Ex 88 Ex 89 Ex 90
II) Logarithmic Functions
25) Differentiating Logarithmic Functions: Level 1	Ex 91 Ex 92 Ex 93
26) Differentiating Logarithmic Functions: Level 2	Ex 94 Ex 95 Ex 96 Ex 97
27) Differentiating Logarithm Functions of the Form \(\log_a(x)\)	Ex 98 Ex 99 Ex 100 Ex 101
III) Trigonometric Functions
28) Differentiating Trigonometric Functions: Level 1	Ex 102 Ex 103
29) Differentiating Trigonometric Functions: Level 2	Ex 104 Ex 105 Ex 106 Ex 107
30) Finding the Slope of a Tangent Line of an Implicit Function	Ex 108
D) Second Derivative
I) Definition
31) Calculating the First and Second Derivative: Level 1	Ex 109 Ex 110 Ex 111
32) Calculating the First and Second Derivative: Level 2	Ex 112 Ex 113 Ex 114

Lesson
Text book

Exercises Correction
A) Derivative
    I) Rate of Change
      1) Finding Rate of Change Ex 1 Ex 2 Ex 3 Ex 4
      2) Finding Rate of Change from a Graph Ex 5 Ex 6 Ex 7 Ex 8
      3) Modeling with Rates of Change Ex 9 Ex 10 Ex 11 Ex 12
      4) Modeling with Rates of Change Ex 13 Ex 14 Ex 15
    II) Limit Definition of the Derivative
      5) Conjecturing the Derivative at a Point Ex 16 Ex 17 Ex 18
      6) Finding the Derivative Graphically Ex 19 Ex 20 Ex 21 Ex 22
    III) Derivative Function
      7) Finding the Derivative from First Principles Ex 23 Ex 24 Ex 25 Ex 26 Ex 27
      8) Interpreting the Graph of the Derivative Ex 28 Ex 29 Ex 30
      9) Finding the Tangent Slope Using the Derivative Function Ex 31 Ex 32 Ex 33
    IV) Conditions of Differentiability
      10) Identifying Differentiability from a Graph Ex 34 Ex 35 Ex 36
B) Rules of Differentiation
    I) Basic Rules and Power Functions
      11) Proving Basic Rules and Power Functions Ex 37 Ex 38 Ex 39 Ex 40
      12) Applying the Power Rule Ex 41 Ex 42 Ex 43 Ex 44 Ex 45
      13) Differentiating Polynomial Functions Ex 46 Ex 47 Ex 48 Ex 49
      14) Differentiating Functions with Fractional and Negative Exponents Ex 50 Ex 51 Ex 52 Ex 53
      15) Expanding Before Differentiating Ex 54 Ex 55 Ex 56 Ex 57
    II) Chain Rule
      16) Forming Composite Functions Ex 58

Definition Polygon

A polygon is a flat, closed shape made of straight sides that do not cross each other.

Ex 59 Ex 60
      17) Decomposing Composite Functions Ex 61 Ex 62 Ex 63 Ex 64
      18) Differentiating with the Chain Rule Ex 65

Definition Polygon

A polygon is a flat, closed shape made of straight sides that do not cross each other.

Ex 66 Ex 67
    III) Product Rule
      19) Differentiating with the Product Rule Ex 68 Ex 69 Ex 70 Ex 71
    IV) Quotient Rule
      20) Differentiating with the Quotient Rule Ex 72 Ex 73 Ex 74 Ex 75
    V) Implicit Differentiation
      21) Finding the Derivative of an Implicit Function Ex 76 Ex 77 Ex 78
      22) Finding the Slope of a Tangent Line of an Implicit Function Ex 79 Ex 80 Ex 81
C) Derivatives of Standard Functions
    I) Exponential Functions
      23) Differentiating Exponential Functions: Level 1 Ex 82 Ex 83 Ex 84 Ex 85
      24) Differentiating Exponential Functions: Level 2 Ex 86 Ex 87 Ex 88 Ex 89 Ex 90
    II) Logarithmic Functions
      25) Differentiating Logarithmic Functions: Level 1 Ex 91 Ex 92 Ex 93
      26) Differentiating Logarithmic Functions: Level 2 Ex 94 Ex 95 Ex 96 Ex 97
      27) Differentiating Logarithm Functions of the Form \(\log_a(x)\) Ex 98 Ex 99 Ex 100 Ex 101
    III) Trigonometric Functions
      28) Differentiating Trigonometric Functions: Level 1 Ex 102 Ex 103
      29) Differentiating Trigonometric Functions: Level 2 Ex 104 Ex 105 Ex 106 Ex 107
      30) Finding the Slope of a Tangent Line of an Implicit Function Ex 108
D) Second Derivative
    I) Definition
      31) Calculating the First and Second Derivative: Level 1 Ex 109 Ex 110 Ex 111
      32) Calculating the First and Second Derivative: Level 2 Ex 112 Ex 113 Ex 114