If z = x²y + xy², then at point (1,1):

For f(x,y) = x² + y²:

The function f(x,y) = x²y is:

The Taylor series expansion of f(x,y) = x + y about (0,0):

For z = x² - y²:

For f(x,y) =sin(xy)eˣ⁺ʸ, at point (0,0):

If z = f(x,y) where x = r⋅cos θ, y = r⋅sin θ,then:

For f(x,y) = (x² - y²)/(x² + y²):

For the function f(x,y) = x² + xy + y²:

For the transformation x = u² - v², y = 2uv: