URGENT what is the second derivative with respect to x and with respect to y of 2-ln[1+(x-2)^2+(y-2)^2]

Answer 1

partial derivative of f(x,y) wrt x is -2x/(1+(x-2)²+(y-2)²)

The second partial derivative of f(x,y) wrt x is [(1+(x-2)²+(y-2)²)(-2)+2x(2x)]/(1+(x-2)²+(y-2)²)²

The second derivative wrt y is the same as x with y and x switched (symmetry)

The mixed derivative d²f/dxdy is 4xy/(1+(x-2)²+(y-2)²)²