Stewart6e3_5 - MATH 191, Sections 1 and 3 Calculus I Fall...

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Unformatted text preview: MATH 191, Sections 1 and 3 Calculus I Fall 2007 Section 3.5: Sneakiness in Calcland: Implicit Differentiation Sometimes the relationship between two variables, x and y , say, is most easily expressed by means of a relation which is not a function. For instance, the relation x 2 + y 2 = 25 describes a circle centered at the origin of the plane with radius 5. The same curve would take two different functions to describe it, since the graph consisting of the circle above is not the graph of a function. Lets see how this works in the space below: It still makes sense to talk about the rate of change of y with respect to x , however, since these two variables are related to one another. Furthermore, it still makes sense to talk about lines tangent to the curve given by the relationship above. In other words, we still want to be able to talk about dy dx . differentiation is the means by which we will compute dy dx without solving for y in terms of x . We merely think of y as a function of...
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Stewart6e3_5 - MATH 191, Sections 1 and 3 Calculus I Fall...

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