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# Implicit Differentiation (3

By Tiffany Arnold,2014-01-07 06:39
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Implicit Differentiation (3

Name ______________________ AP Calculus AB

Chapter 3 Day 4 Implicit Differentiation (3.7)

We often have equations of graphs that don’t come in the convenient explicit form

33 . For example: . In such a case we must use what is called ;；yfxx4y6y8

implicit differentiation:

Steps for Implicit Differentiation: 1) Differentiate both sides with respect to x. dy on one side of the equation. 2) Collect the terms with dx dy 3) Factor out . dx

dy 4) Solve for . dx

dy2Example: Find if and find the slope of the tangent when . yxx4dx

22Example: Find the slope of the circle at the point ;；. xy253,4

Name ______________________ AP Calculus AB

Chapter 3 Day 4 Implicit Differentiation (3.7)

dyExample: Show that the slope is defined at every point on the graph of dx

2 . 2yxsiny

22Example: Find the tangent and normal to the ellipse at . ;；xxyy71,2

2dy32Example: Find the second derivative if . 2x3y82dx

Homework: pg 155 1 35 odd, 37a, 41, 49

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