1. The problem is to find the functions $g$ and $h$ given $f=\sqrt{x^2+y^2}$. 2. Typically, $g$ and $h$ refer to the partial derivatives of $f$ with respect to $x$ and $y$, respectively. 3. The formula for partial derivatives is: $$g = \frac{\partial f}{\partial x}, \quad h = \frac{\partial f}{\partial y}$$ 4. Given $f=\sqrt{x^2+y^2} = (x^2 + y^2)^{1/2}$, apply the chain rule: $$g = \frac{1}{2}(x^2 + y^2)^{-1/2} \cdot 2x = \frac{x}{\sqrt{x^2 + y^2}}$$ $$h = \frac{1}{2}(x^2 + y^2)^{-1/2} \cdot 2y = \frac{y}{\sqrt{x^2 + y^2}}$$ 5. Therefore, the functions are: $$g = \frac{x}{\sqrt{x^2 + y^2}}, \quad h = \frac{y}{\sqrt{x^2 + y^2}}$$ These represent the rates of change of $f$ with respect to $x$ and $y$ respectively.