Day 22 - Implicit Differentiation - 09.16.15


Bell Ringer

Note: Some of these are problems you have not seen yet.
Find using the derivative operator.
Hint: Try to get y by itself on one side of the equation (if you can).

    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

  • Pre-calculus
    • Slope
    • Equation of a Line
    • Secant Line vs. Tangent Line (video)
  • Tangent Line
    • How can the slope of one point be found?
    • Finding the derivative of polynomials using limits (example)
  • Basic Differentiation Rules
    • How can derivatives be calculated using basic differentiation rules?

  • Challenge 6
    • Find the derivative of the following:
    • Hints will be given as needed.
    • No computers allowed!

Exit Ticket
  • Posted on the board at the end of the block.

  • N/A

Lesson Objectives
  • How can implicit differentiation be used to find derivatives?

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.9
    • Apply formulas to find derivatives.
      • Includes:
        • derivatives of algebraic, trigonometric, exponential, logarithmic, and inverse trigonometric functions
        • derivations of sums, products, quotients, inverses, and composites (chain rule) of elementary functions
        • derivatives of implicitly defined functions