# 13.3 Partial derivatives For an animation of this concept visit http://www.math.umn.edu/~rogness/multivar/dirderiv.shtml.

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13.3 Partial derivatives For an animation of this concept visit

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 Note: is also written as (eff sub ecks)

Notation for First Partial Derivatives

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?

Definition of Partial Derivatives of a Function of Two Variables

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

Diagram for example 2

Example 2 solution

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

Solution to example 3

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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