Find out the answer to "Given f(x,y)=−3x2−4xy3−y4, find fxx(x,y)= fxy(x,y)="

babeeb0oL

Answered question

2021-10-15

Given $f (x, y) = - 3 x^{2} - 4 x y^{3} - y^{4}$ , find
$f_{x x} (x, y) =$
$f_{x y} (x, y) =$

Answer & Explanation

Leonard Stokes

Skilled2021-10-16Added 98 answers

Step 1
Consider the given function.
$f (x, y) = - 3 x^{2} - 4 x y^{3} - y^{4}$
The required functions $f_{x x} (x, y) and f_{x y} (x, y)$ are second-order partial derivatives.
Step 2
First find $f_{x} (x, y)$ .
$f_{x} (x, y)$ is the partial derivative of the function with respect to x keeping y as constant. So
$f_{x} (x, y) = - 3 \cdot 2 x - 4 y^{3} \cdot 1 - 0$
$= - 6 x - 4 y^{3}$
Step 3
$f_{x x} (x, y)$ is the partial derivative of $f_{x} (x, y) = - 6 x - 4 y^{3}$ with respect to x and keeping y as constant.
$f_{x x} (x, y) = - 6 \cdot 1 - 0$
=-6
$f_{x y} (x, y)$ is the partial derivative of $f_{x} (x, y) = - 6 x - 4 y^{3}$ with respect to y and keeping x as constant.
$f_{x y} (x, y) = - 0 - 4 \cdot 3 y^{2}$
$= - 12 y^{2}$
Therefore, $f_{x x} (x, y) = - 6 and f_{x y} (x, y) = - 12 y^{2}$ .

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

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