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## Homework Statement

Calculate the gradient vector at the point [tex]S[/tex] for the function, [tex]f(x,y,z)=x-\sqrt{z^2 - y^2}; S(x,y,z)=(4, 8, -6)[/tex].

**2. The attempt at a solution**

[tex]\frac{\partial f}{\partial x} = 1[/tex]

[tex]\frac{\partial f}{\partial y} = \frac{y}{\sqrt{z^2-y^2}}[/tex]

[tex]\frac{\partial f}{\partial z} = -\frac{z}{\sqrt{z^2-y^2}}[/tex]

Therefore at Point [tex]S[/tex]:

[tex]\frac{\partial f}{\partial x} = 1[/tex]

[tex]\frac{\partial f}{\partial y} = \frac{-6}{\sqrt{36-64}} = \frac{-6}{\sqrt{-28}}[/tex]

**3. The problem that I'm having**

When I put the point values of Point [tex]S[/tex] into the equation, I get a negative square root in the denominator. Where am I going wrong? Thanks in advance.