Day 18 - Implicit Differentiation - 02.03.15


Bell Ringer

Calculate for the following:

    1. x

    2. y

    3. 1

    4. 0

    5. none of the above

    1. 2

    2. 0

    3. none of the above

    1. none of the above

    1. none of the above

    1. none of the above

  • Prerequisite
    • Secant Lines (video)
    • Tangent Lines (video)
      • Equation of a Tangent Line (video)
  • Derivative (video)
    • Derivative Rules
      • Constant Rule (video)
      • Power Rule (video)
      • Constant Multiple Rule (video)
      • Sum and Difference Rule (video)
    • Derivative of Sine and Cosine Functions
    • Higher Order Derivatives
    • Rates of Change
      • Position Function
      • Velocity Function
      • Acceleration Function
    • Product Rule (video)
    • Quotient Rule (video)
    • Chain Rule (video)


Exit Ticket
  • Posted on the board at the end of the block
Lesson Objectives
  • How can implicit differentiation be used to find the derivative?

In-Class Help Requests

  • APC.5
    • Investigate derivatives presented in graphic, numerical, and analytic contexts and the relationship between continuity and differentiability.
      • The derivative will be defined as the limit of the difference quotient and interpreted as an instantaneous rate of change.
  • APC.6
    • ​The student will investigate the derivative at a point on a curve.
      • Includes:
        • finding the slope of a curve at a point, including points at which the tangent is vertical and points at which there are no tangents
        • using local linear approximation to find the slope of a tangent line to a curve at the point
        • ​defining instantaneous rate of change as the limit of average rate of change
        • approximating rate of change from graphs and tables of values.
  • APC.7
    • Analyze the derivative of a function as a function in itself.
      • Includes:
        • comparing corresponding characteristics of the graphs of f, f', and f''
        • ​defining the relationship between the increasing and decreasing behavior of f and the sign of f'
        • ​translating verbal descriptions into equations involving derivatives and vice versa
        • defining the relationship between the concavity of f and the sign of f "
  • APC.9
    • Apply formulas to find derivatives.
      • Includes:
        • derivatives of algebraic and trigonometric functions
        • derivations of sums, products, quotients, inverses, and composites (chain rule) of elementary functions
        • derivatives of implicitly defined functions
        • higher order derivatives of algebraic and trigonometric functions

Past Checkpoints