Help with a partial derivative question, thanks.

In summary, we need to use the table of values of f(x,y) to estimate the values of fx(4.2, 4) and fxy(4, 4). To find fxy, we can use the formula (fx+y,x+y + fx-y,x-y)/4, where fx+y represents the change in fx when both x and y increase, fx-y represents the change in fx when x increases but y decreases, and x+y and x-y represent the new values of x and y respectively.
  • #1
kidzonety
5
0
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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  • #2
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:
 

FAQ: Help with a partial derivative question, thanks.

1. What is a partial derivative?

A partial derivative is a mathematical concept used in multivariable calculus to calculate the rate of change of a function with respect to one of its variables, while holding all other variables constant. It is denoted by ∂ (the partial derivative symbol) and is used to analyze how a function changes in multiple directions.

2. How do I solve a partial derivative question?

To solve a partial derivative question, you will need to use the definition of a partial derivative and various rules of differentiation, such as the power rule, product rule, and chain rule. You will also need to understand the concept of holding variables constant and how to differentiate with respect to a specific variable.

3. What is the purpose of finding a partial derivative?

The purpose of finding a partial derivative is to determine the rate of change of a function in a specific direction. It is useful in many fields, such as physics, economics, and engineering, where functions have multiple variables and their rates of change need to be analyzed.

4. Can you provide an example of a partial derivative question?

Sure, an example of a partial derivative question could be: Find the partial derivative of f(x,y) = xy^2 with respect to x. To solve this, you would use the product rule and the power rule to get ∂f/∂x = y^2.

5. How can I use partial derivatives in real-life applications?

Partial derivatives have many real-life applications, such as determining optimal production levels in economics, calculating the direction of maximum change in physics, and optimizing processes in engineering. They can also be used in fields like finance, meteorology, and genetics to analyze complex systems and make predictions.

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