1. The problem asks to find the derivative of the function $6xy$ with respect to both $x$ and $y$. 2. Since $6xy$ is a product of two variables, we use partial derivatives. 3. The partial derivative with respect to $x$ treats $y$ as a constant: $$\frac{\partial}{\partial x}(6xy) = 6y$$ 4. The partial derivative with respect to $y$ treats $x$ as a constant: $$\frac{\partial}{\partial y}(6xy) = 6x$$ 5. So, the derivatives are: - $\frac{\partial}{\partial x}(6xy) = 6y$ - $\frac{\partial}{\partial y}(6xy) = 6x$ This means the rate of change of $6xy$ with respect to $x$ is $6y$, and with respect to $y$ is $6x$.