Help with a partial derivative question, thanks.

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SUMMARY

This discussion focuses on estimating partial derivatives using a table of values for the function f(x,y). The user seeks assistance specifically with calculating the mixed partial derivative fxy at the point (4,4). A formula is provided for calculating fxy, which is fxy = (fx+y,x+y + fx-y,x-y)/4, indicating the relationship between the first and mixed partial derivatives. The conversation emphasizes the importance of understanding both fx and fxy in multivariable calculus.

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  • Understanding of multivariable calculus concepts, specifically partial derivatives.
  • Familiarity with the notation and calculation of first partial derivatives (fx, fy).
  • Knowledge of mixed partial derivatives and their significance in calculus.
  • Ability to interpret and utilize tabular data for function values.
NEXT STEPS
  • Study the derivation and application of mixed partial derivatives in multivariable calculus.
  • Learn how to construct and interpret tables of values for functions of two variables.
  • Explore the implications of Clairaut's theorem on the equality of mixed partial derivatives.
  • Practice calculating both first and mixed partial derivatives using various functions.
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Students and educators in mathematics, particularly those studying multivariable calculus, as well as anyone looking to deepen their understanding of partial derivatives and their applications.

kidzonety
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Use the table of values of f(x,y) to estimate the values of each of the following partial derivatives.


y=4.2 || 2.75262 ||| 0.27222 ||| 0.27107
y=4 ||| 5.74559 ||| 2.84839 ||| 0.64973
y=3.8 || 7.42708 ||| 5.84832 ||| 3.25237
||||||||| x=3.8 |||||| x=4 ||||||| x=4.2


fx(4.2 , 4) =
fxy(4 , 4) =

I know how to get fx, but don't know how to get fxy.
Hopefully you guys can teach me.
Thanks a lot!
 
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Welcome to PF!

Hi kidzonety! Welcome to PF! :smile:

(try using the X2 tag just above the Reply box :wink:)
kidzonety said:
I know how to get fx, but don't know how to get fxy.

Do you know how to get fxx?

If so, use fxy = (fx+y,x+y + fx-y,x-y)/4 :wink:
 

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