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13.3 Partial derivatives For an animation of this concept visit http://www.math.umn.edu/~rogness/multivar/dirderiv.shtml. When we have functions with more than one variable, we can find partial derivatives by holding all the variables but one constant. z. 100. 10. y. 10. x.

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  1. 13.3 Partial derivativesFor an animation of this concept visithttp://www.math.umn.edu/~rogness/multivar/dirderiv.shtml

  2. When we have functions with more than one variable, we can find partial derivatives by holding all the variables but one constant. z 100 10 y 10 x (eff sub ecks) Note: is also written as

  3. Notation for First Partial Derivatives

  4. would give you the slope of the tangent in the plane y=0 or in any plane with constant y. z 100 10 y 10 x In other words, how is changing one variable going to change the value of the function?

  5. Definition of Partial Derivatives of a Function of Two Variables

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

  7. Diagram for example 2

  8. Example 2 solution

  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

  10. Solution to example 3

  11. 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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