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Differential Calculus

Learning tasks
                                  
Lesson Summary
Text book
Exercises Correction
A) Derivative
    I) Rate of Change
      1) Finding Rate of ChangeEx 1 Ex 2 Ex 3 Ex 4
      2) Finding Rate of Change from a GraphEx 5 Ex 6 Ex 7 Ex 8
      3) Modeling with Rates of ChangeEx 9 Ex 10 Ex 11 Ex 12
      4) Modeling with Rates of ChangeEx 13 Ex 14 Ex 15
    II) Limit Definition of the Derivative
      5) Conjecturing the Derivative at a PointEx 16 Ex 17 Ex 18
      6) Finding the Derivative GraphicallyEx 19 Ex 20 Ex 21 Ex 22
      7) Finding the Derivative at a PointEx 23 Ex 24 Ex 25
    III) Derivative Function
      8) Finding the Derivative from First PrinciplesEx 26 Ex 27 Ex 28 Ex 29 Ex 30
      9) Interpreting the Graph of the DerivativeEx 31 Ex 32 Ex 33
      10) Finding the Tangent Slope Using the Derivative FunctionEx 34 Ex 35 Ex 36
    IV) Conditions of Differentiability
      11) Identifying Differentiability from a GraphEx 37 Ex 38 Ex 39
      12) Proving Non-Differentiability at a PointEx 40 Ex 41
B) Rules of Differentiation
    I) Basic Rules and Power Functions
      13) Proving Basic Rules and Power FunctionsEx 42 Ex 43 Ex 44 Ex 45
      14) Applying the Power RuleEx 46 Ex 47 Ex 48 Ex 49 Ex 50
      15) Differentiating Polynomial FunctionsEx 51 Ex 52 Ex 53 Ex 54
      16) Differentiating Functions with Fractional and Negative ExponentsEx 55 Ex 56 Ex 57 Ex 58
      17) Expanding Before DifferentiatingEx 59 Ex 60 Ex 61 Ex 62
    II) Chain Rule
      18) Forming Composite FunctionsEx 63 Ex 64 Ex 65 Ex 66
      19) Decomposing Composite FunctionsEx 67 Ex 68 Ex 69 Ex 70
      20) Differentiating with the Chain RuleEx 71 Ex 72 Ex 73 Ex 74
    III) Product Rule
      21) Differentiating with the Product RuleEx 75 Ex 76 Ex 77 Ex 78
    IV) Quotient Rule
      22) Differentiating with the Quotient RuleEx 79 Ex 80 Ex 81 Ex 82
    V) Implicit Differentiation
      23) Finding the Derivative of an Implicit FunctionEx 83 Ex 84 Ex 85
      24) Finding the Slope of a Tangent Line of an Implicit FunctionEx 86 Ex 87 Ex 88
C) Derivatives of Standard Functions
    I) Exponential Functions
      25) Differentiating Exponential Functions: Level 1Ex 89 Ex 90 Ex 91 Ex 92
      26) Differentiating Exponential Functions: Level 2Ex 93 Ex 94 Ex 95 Ex 96 Ex 97
    II) Logarithmic Functions
      27) Differentiating Logarithmic Functions: Level 1Ex 98 Ex 99 Ex 100
      28) Differentiating Logarithmic Functions: Level 2Ex 101 Ex 102 Ex 103 Ex 104
      29) Differentiating Logarithm Functions of the Form \(\log_a(x)\)Ex 105 Ex 106 Ex 107 Ex 108
    III) Trigonometric Functions
      30) Differentiating Trigonometric Functions: Level 1Ex 109 Ex 110 Ex 111
      31) Differentiating Trigonometric Functions: Level 2Ex 112 Ex 113 Ex 114 Ex 115
      32) Finding the Slope of a Tangent Line of an Implicit FunctionEx 116
      33) Differentiating Other Trigonometric Functions: Level 1Ex 117 Ex 118 Ex 119
      34) Differentiating Other Trigonometric Functions: Level 2Ex 120 Ex 121 Ex 122
    IV) Inverse Trigonometric Functions
      35) Differentiating Inverse Trigonometric Functions: Level 1Ex 123 Ex 124 Ex 125
      36) Differentiating Inverse Trigonometric Functions: Level 2Ex 126 Ex 127 Ex 128
D) Second Derivative
    I) Definition
      37) Calculating the First and Second Derivative: Level 1Ex 129 Ex 130 Ex 131
      38) Calculating the First and Second Derivative: Level 2Ex 132 Ex 133 Ex 134
E) Finding Limits of Indeterminate Forms
    I) L'Hôpital's Rule
      39) Applying L'Hôpital's Rule: Level 1Ex 135 Ex 136 Ex 137 Ex 138 Ex 139
      40) Applying L'Hôpital's Rule: Level 2Ex 140 Ex 141 Ex 142