Find both first partial derivatives. \[ f(x, y)=6 x-2 y+3 \]

To find the first partial derivatives of the function \( f(x, y) = 6x - 2y + 3 \), we need to differentiate with respect to each variable while treating the other variable as a constant. The first partial derivative with respect to \( x \) is: \[ \frac{\partial f}{\partial x} = 6 \] The first partial derivative with respect to \( y \) is: \[ \frac{\partial f}{\partial y} = -2 \] So, the first partial derivatives are \( \frac{\partial f}{\partial x} = 6 \) and \( \frac{\partial f}{\partial y} = -2 \).