Answered: "Find the four second partial derivatives of f(x,y)=x2sin⁡y"

Answered question

2021-07-01

Find the four second partial derivatives of $f (x, y) = x^{2} \sin y$

Jeffrey Jordon

Expert2021-07-15Added 2605 answers

Step 1

The given function is $f (x, y) = x^{2} \sin y$

This implies that,

$f_{x} = 2 x \sin y$

$f_{y} = x^{2} \cos y$

Step 2

Now obtain the second derivatives as follows.

$f_{x x} = 2 \sin y$

$f_{y y} = - x^{2} \sin y$

$f_{x y} = 2 x \cos y$

$f_{y x} = 2 x \cos y$

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