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

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1. Write the function:
   $$
   f(x, y) = 6x - 2y + 3
   $$

2. Compute the partial derivative with respect to $$ x $$ ($$ f_x(x, y) $$):
   - The derivative of $$ 6x $$ with respect to $$ x $$ is $$ 6 $$.
   - The term $$ -2y $$ is treated as a constant with respect to $$ x $$ so its derivative is $$ 0 $$.
   - The constant $$ 3 $$ also has derivative $$ 0 $$.
   
   Therefore,
   $$
   f_x(x, y) = 6
   $$

3. Compute the partial derivative with respect to $$ y $$ ($$ f_y(x, y) $$):
   - The derivative of $$ -2y $$ with respect to $$ y $$ is $$ -2 $$.
   - The term $$ 6x $$ is treated as a constant with respect to $$ y $$ so its derivative is $$ 0 $$.
   - The constant $$ 3 $$ also has derivative $$ 0 $$.
   
   Therefore,
   $$
   f_y(x, y) = -2
   $$
The partial derivatives are: - $$ f_x(x, y) = 6 $$ - $$ f_y(x, y) = -2 $$

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

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