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Published byZoe McKenzie Modified over 5 years ago

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13.3 Partial derivatives For an animation of this concept visit

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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)

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**Notation for First Partial Derivatives**

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**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?

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**Definition of Partial Derivatives of a Function of Two Variables**

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**Example 2 f(x,y) = e x y , find fx and fy 2**

And evaluate each at the point (1,ln2) 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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Definition of the Derivative Using Average Rate () a a+h f(a) Slope of the line = h f(a+h) Average Rate of Change = f(a+h) – f(a) h f(a+h) – f(a) h.

Definition of the Derivative Using Average Rate () a a+h f(a) Slope of the line = h f(a+h) Average Rate of Change = f(a+h) – f(a) h f(a+h) – f(a) h.

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