Question

How do I differentiate fx and fy f(x,y)=√(1+x^2 +y^2)

Answer 1

f = (1+x^2+y^2)^.5
df/dx = .5 (1+x^2+y^2)^-.5 * d/dx (1+x^2+y^2)
= .5 (1+x^2+y^2)^-.5 (0 + 2x + 2 y dy/dx)
= (x + y dy/dx) / √(1+x^2 +y^2)

Answer 2

If you're looking for partial derivatives, then as Damon showed,
Fx = x/√(1+x^2 +y^2)
Fy = y/√(1+x^2 +y^2)