### Day 27 - Implicit Differentiation - 02.17.15

Update

Bell Ringer

Calculate for the following:
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

Lesson
• Implicit Differentiation

Exit Ticket
• Posted on the board at the end of the block
Lesson Objectives
• How is implicit differentiation used to solve problems?

#### 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.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
• Derivative
• Derivative Rules
• Higher Order Derivatives
• Rates of Change
• Position Function
• Velocity Function
• Acceleration Function
• Product Rule
• Quotient Rule
• Chain Rule
• Implicit Differentiation
• Checkpoints
• A - page 146 #6
• B - page 146 #10
• C - page 146 #26
• D - page 146 #30
• E - page 147 #48
• F - page 147 #52
• G - page 147 #66
• H - page 148 #74
• I - page 148 #78
• Related Rates
• Checkpoints
• A - page 154 #2
• B - page 154 #16
• C - page 154 #18
• D - page 154 #20
• E - page 154 #14