## Homework Statement

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

2. The attempt at a solution
$$\frac{\partial f}{\partial x} = 1$$
$$\frac{\partial f}{\partial y} = \frac{y}{\sqrt{z^2-y^2}}$$
$$\frac{\partial f}{\partial z} = -\frac{z}{\sqrt{z^2-y^2}}$$
Therefore at Point $$S$$:
$$\frac{\partial f}{\partial x} = 1$$
$$\frac{\partial f}{\partial y} = \frac{-6}{\sqrt{36-64}} = \frac{-6}{\sqrt{-28}}$$

3. The problem that I'm having
When I put the point values of Point $$S$$ into the equation, I get a negative square root in the denominator. Where am I going wrong? Thanks in advance.