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

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  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)

  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)

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