If f(x,y)=x2 +y2, then fxy(x,y) =
Question
If f(x,y)=x2 +y2, then fxy(x,y) =
Solution 1
To find the mixed partial derivative fxy(x,y) of the function f(x,y) = x^2 + y^2, we first need to find the partial derivatives fx and fy.
Step 1: Find fx(x,y) The partial derivative of f with respect to x, denoted fx, is the derivative of f(x,y) with respect to x, treating y as a constant.
fx(x,y) = 2x
Step 2: Find fxy(x,y) The mixed partial derivative fxy is the derivative of fx with respect to y. Since fx does not contain y, its derivative with respect to y is 0.
So, fxy(x,y) = 0.
Solution 2
The function given is f(x,y) = x^2 + y^2.
The partial derivative of f with respect to x is fx = 2x.
The partial derivative of f with respect to y is fy = 2y.
The second order mixed partial derivative fxy is the partial derivative of fx with respect to y.
Since fx = 2x is a constant with respect to y, its derivative with respect to y is zero.
Therefore, fxy(x,y) = 0.
Solution 3
The function f(x,y) = x^2 + y^2 is given. We are asked to find the mixed partial derivative fxy(x,y).
Step 1: Find the partial derivative of f with respect to x, denoted as fx(x,y).
fx(x,y) = 2x
Step 2: Find the partial derivative of fx with respect to y, denoted as fxy(x,y).
fxy(x,y) = 0
So, the mixed partial derivative fxy(x,y) of the function f(x,y) = x^2 + y^2 is 0.
Solution 4
The function f(x,y) = x^2 + y^2 is given. We are asked to find the mixed partial derivative fxy(x,y).
Step 1: Find the partial derivative of f with respect to x, denoted as fx(x,y).
fx(x,y) = 2x
Step 2: Find the partial derivative of fx with respect to y, denoted as fxy(x,y).
fxy(x,y) = 0
So, the mixed partial derivative fxy(x,y) of the function f(x,y) = x^2 + y^2 is 0.
Solution 5
The function given is f(x,y) = x^2 + y^2.
The partial derivative of f with respect to x is fx = 2x.
The partial derivative of f with respect to y is fy = 2y.
The second order mixed partial derivative fxy is the partial derivative of fx with respect to y.
Since fx = 2x is a constant with respect to y, its derivative with respect to y is 0.
So, fxy(x,y) = 0.
Solution 6
The function f(x,y) = x^2 + y^2 is given. We are asked to find the mixed partial derivative fxy(x,y).
Step 1: Find the partial derivative of f with respect to x, denoted as fx(x,y).
fx(x,y) = 2x
Step 2: Find the partial derivative of fx with respect to y, denoted as fxy(x,y).
fxy(x,y) = 0
So, the mixed partial derivative fxy(x,y) of the function f(x,y) = x^2 + y^2 is 0.
Solution 7
To find the mixed partial derivative fxy(x,y) of the function f(x,y) = x^2 + y^2, we first need to find the partial derivative fx and then find the derivative of fx with respect to y.
Step 1: Find fx(x,y) The partial derivative of f with respect to x, denoted fx, is the derivative of f(x,y) with respect to x, treating y as a constant.
fx(x,y) = 2x
Step 2: Find fxy(x,y) Now, we find the derivative of fx with respect to y, treating x as a constant. Since fx does not contain y, its derivative with respect to y is 0.
fxy(x,y) = 0
So, the mixed partial derivative fxy(x,y) of the function f(x,y) = x^2 + y^2 is 0.
Solution 8
To find fxy(x,y), we first need to understand what it represents. It is the second order mixed partial derivative of the function f(x,y) with respect to x and y.
Here are the steps to find fxy(x,y):
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First, find the first order partial derivative of the function f(x,y) with respect to x. This is denoted as fx(x,y). For the function f(x,y) = x^2 + y^2, the derivative with respect to x is fx(x,y) = 2x.
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Next, find the first order partial derivative of fx(x,y) with respect to y. This is denoted as fxy(x,y). Since fx(x,y) = 2x is a constant with respect to y, its derivative with respect to y is 0.
So, fxy(x,y) = 0.
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