calc notes lecture 12

Calc notes lecture - y and avoid implicit differentiation However that won’t always be the case For example it is difficult to express y as a

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Lecture Section Objectives Assignment 12 2.7 Implicit Differentiation 2.7: 1-39 eoo. Understanding Goals: 1. Understand the difference between explicit form and implicit form of functions. 2. Understand how to find derivatives explicitly. 3. Understand how to find derivatives implicitly. 4. Understand how to use implicit differentiation to answer questions about real-life situation Example 1 : Use two ways to find ' for 1 y xy = . a) Solve for y b) Without Solving for y The process that we used in the second solution to the previous example is called implicit differentiation . In the previous example we were able to just solve for
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Unformatted text preview: y and avoid implicit differentiation. However, that won’t always be the case. For example it is difficult to express y as a function of x explicitly if 3 3 2 1 x y y-+ = . Example 2 : Differentiating with respect to x : (a) 3 2 x (b) 2 3 y (c) x y + 2 (d) xy 2 1 Example 3 : Use implicit differentiation to find ' y : (a) 2 2 1 x y + = (b) 2 5 3 x xy y-+ = 2 (c) 3 1 2 x y xy + = + (d) 5 2 6 3 2 x y-= 3 Example 4 : Find the tangent line to the graph given by 2 2 2 2 ( ) x x y y + = at the point 2 2 , 2 2 . 4...
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This note was uploaded on 04/17/2008 for the course MAT 111 taught by Professor Fan during the Spring '08 term at Union.

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Calc notes lecture - y and avoid implicit differentiation However that won’t always be the case For example it is difficult to express y as a

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