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13.3 Partial derivatives For an animation of this concept visit

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y x z When we have functions with more than one variable, we can find partial derivatives by holding all the variables but one constant. Note:is also written as (eff sub ecks)

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Notation for First Partial Derivatives

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y x z would give you the slope of the tangent in the plane y=0 or in any plane with constant y. In other words, how is changing one variable going to change the value of the function?

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Definition of Partial Derivatives of a Function of Two Variables

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f(x,y) = e x y, find f x and f y And evaluate each at the point (1,ln2) 2 Example 2

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Diagram for example 2

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Example 2 solution

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Example 3 Find the slope in the x-direction and in the y-direction of the surface given by When x=1 and y=2

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Solution to example 3

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Example 4 Find the slope of the given surface in the x-direction and the y-direction at the point (1,2,1)

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