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).
x y 1 0 none of the above
2 0 none of the above
none of the above
none of the above
 none of the above
Review
 Precalculus
 Slope
 Equation of a Line
 Secant Line vs. Tangent Line (video)
 Tangent Line
 How can the slope of one point be found?
 Equation of a Tangent Line (video)
 Derivative (video) (checkpoints)
 How are derivatives related to tangent lines?
 Finding the derivative of polynomials using limits (example)
 Basic Differentiation Rules
 How can derivatives be calculated using basic differentiation rules?
 Product Rule/Quotient Rule (checkpoints)
 How can derivatives of the product/quotient of functions be calculated?
Lesson Challenge 6
 Find the derivative of the following:
 Hints will be given as needed.
 No computers allowed!
 Implicit Differentiation (video)
Exit Ticket
 Posted on the board at the end of the block.
Homework

Lesson Objectives
 How can implicit differentiation be used to find derivatives?
Standard(s)
 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
