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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
    III) Derivative Function
      7) Finding the Derivative from First PrinciplesEx 23 Ex 24 Ex 25 Ex 26 Ex 27
      8) Interpreting the Graph of the DerivativeEx 28 Ex 29 Ex 30
      9) Finding the Tangent Slope Using the Derivative FunctionEx 31 Ex 32 Ex 33
    IV) Conditions of Differentiability
      10) Identifying Differentiability from a GraphEx 34 Ex 35 Ex 36
B) Rules of Differentiation
    I) Basic Rules and Power Functions
      11) Proving Basic Rules and Power FunctionsEx 37 Ex 38 Ex 39 Ex 40
      12) Applying the Power RuleEx 41 Ex 42 Ex 43 Ex 44 Ex 45
      13) Differentiating Polynomial FunctionsEx 46 Ex 47 Ex 48 Ex 49
      14) Differentiating Functions with Fractional and Negative ExponentsEx 50 Ex 51 Ex 52 Ex 53
      15) Expanding Before DifferentiatingEx 54 Ex 55 Ex 56 Ex 57
    II) Chain Rule
      16) Forming Composite FunctionsEx 58 Ex 59 Ex 60 Ex 61
      17) Decomposing Composite FunctionsEx 62 Ex 63 Ex 64 Ex 65
      18) Differentiating with the Chain RuleEx 66 Ex 67 Ex 68 Ex 69
    III) Product Rule
      19) Differentiating with the Product RuleEx 70 Ex 71 Ex 72 Ex 73
    IV) Quotient Rule
      20) Differentiating with the Quotient RuleEx 74 Ex 75 Ex 76 Ex 77
    V) Implicit Differentiation
      21) Finding the Derivative of an Implicit FunctionEx 78 Ex 79 Ex 80
      22) Finding the Slope of a Tangent Line of an Implicit FunctionEx 81 Ex 82 Ex 83
C) Derivatives of Standard Functions
    I) Exponential Functions
      23) Differentiating Exponential Functions: Level 1Ex 84 Ex 85 Ex 86 Ex 87
      24) Differentiating Exponential Functions: Level 2Ex 88 Ex 89 Ex 90 Ex 91 Ex 92
    II) Logarithmic Functions
      25) Differentiating Logarithmic Functions: Level 1Ex 93 Ex 94 Ex 95
      26) Differentiating Logarithmic Functions: Level 2Ex 96 Ex 97 Ex 98 Ex 99
      27) Differentiating Logarithm Functions of the Form \(\log_a(x)\)Ex 100 Ex 101 Ex 102 Ex 103
    III) Trigonometric Functions
      28) Differentiating Trigonometric Functions: Level 1Ex 104 Ex 105
      29) Differentiating Trigonometric Functions: Level 2Ex 106 Ex 107 Ex 108 Ex 109
      30) Finding the Slope of a Tangent Line of an Implicit FunctionEx 110
D) Second Derivative
    I) Definition
      31) Calculating the First and Second Derivative: Level 1Ex 111 Ex 112 Ex 113
      32) Calculating the First and Second Derivative: Level 2Ex 114 Ex 115 Ex 116