Let $z = f(x,y) = 12x^2 - 16xy + 9y^2$. Find the following using the formal definition of the partial derivative.\\
a. $\frac{\partial z}{\partial x}$
b. $\frac{\partial z}{\partial y}$
c. $\frac{\partial f}{\partial x}(-3, -4)$
d. $f_y(3, -1)$\\
a. $\frac{\partial z}{\partial x} = \boxed{}$ \\
b. $\frac{\partial z}{\partial y} = \boxed{}$ \\
c. $\frac{\partial f}{\partial x}(-3, -4) = \boxed{}$ (Simplify your answer.)\\
d. $f_y(3, -1) = \boxed{}$ (Simplify your answer.)