Unit 2: Differentiation

2.1 The Concept of Derivatives

• • • Secant Lines and Tangent Lines (conceptual)

    • Differentiability (conceptual and example problem)

    • Equation of a Tangent Line (conceptual)

    • Equation of a Tangent Line (example problem)

    • Checking a Derivative on a Calculator

    • Finding the Equation of a Tangent Line on a Calculator

    • Derivative (conceptual)

    • Finding Slope at a Point (example problem 1 of 2)

    • Finding Slope at a Point (example problem 2 of 2)

    • Derivatives of a Polynomial using Limits (example problem)

    • Derivatives of the Square Root of x Function Using Limits (example problem)

    • Derivative of Absolute Value Function using Limits (example problem)

    • Derivative of Sine and Cosine (conceptual)

2.2 Derivative Rules

• • Derivative Rules - Constant Rule (conceptual)

  • The Constant Rule (example problem)

  • Derivative Rules - Power Rule (conceptual)

  • The Power Rule (example problem)

  • Derivative Rules - Constant Multiple Rule (conceptual)

  • The Constant Multiple Rule (example problem)

  • Derivative Rules Sum and Difference Rule (conceptual)

  • Derivative of Inverse Sine

  • Exponential and Logarithmic Function Review

  • Derivative and Antiderivative of a^x (conceptual)

  • Derivative and Antiderivative of e^x (conceptual)

  • Differentiation of the Natural Logarithmic Function (conceptual)

  • Derivative Rules - Product Rule (conceptual)

  • Product Rule (example problem)

  • Derivative Rules - Quotient Rule (conceptual)

  • Quotient Rule (example problem)

  • Derivative Rules - Chain Rule (conceptual)

  • Chain Rule (example problem)

  • Differentiation of a^x (example problem)

  • Differentiation of e^x (example problem)

  • Differentiation of the Natural Logarithmic Function (conceptual)

  • Differentiation of Natural Logs (example problem)

  • Derivative of an Inverse Function (example problem)

2.3 Differentiation of Other Forms

• • Implicit Differentiation (example problem)

  • Implicit Differentiation (example 1 of 2)

  • Implicit Differentiation (example 2 of 2)