### Day 22 - Implicit Differentiation - 09.16.15

Update

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. 1. x

2. y

3. 1

4. 0

5. none of the above

2. 1. 2. 3. 2

4. 0

5. none of the above

3. 1. 2. 3. 4. 5. none of the above

4. 1. 2. 3. 4. 5. none of the above

5. 1. 2. 3. 4. 5. none of the above

Review
• 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?

Lesson
• 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.

Homework
• N/A

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

#### In-Class Help Requests

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