13.3 Partial derivatives For an animation of this concept visit rogness/multivar

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Transcript of 13.3 Partial derivatives For an animation of this concept visit rogness/multivar

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13.3 Partial derivatives For an animation of this concept visit http://www.math.umn.edu/~rogness/multivar/dirderiv.shtml Slide 2 y x z 10 100 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) Slide 3 Notation for First Partial Derivatives Slide 4 y x z 10 100 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? Slide 5 Definition of Partial Derivatives of a Function of Two Variables Slide 6 f(x,y) = e x y, find f x and f y And evaluate each at the point (1,ln2) 2 Example 2 Slide 7 Diagram for example 2 Slide 8 Example 2 solution Slide 9 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 Slide 10 Solution to example 3 Slide 11 Example 4 Find the slope of the given surface in the x-direction and the y-direction at the point (1,2,1) Slide 12 Slide 13