Solution assignment 01 Partial differentiation

Calculate the first, second and mixed partial derivatives of the following function.

$f(x,y)=x^2+y^2+2$

This is a relatively simple function. We get:

$f_x=2x+0+0=2x$ (consider $y$ as a constant)

$f_y=0+2y+0=2x$ (consider $x$ as a constant)

$f_{xx}=2$

$f_{yy}=2$

$f_{xy}=f_{yx}=0$

Indeed, we notice that the mixed derivatives are equal.