1-20-25 Latex Scratchwork

$$\frac{\partial f}{\partial x}=3x+2y-1$$ $$\frac{\partial f}{\partial y}=2x+6y+4$$

$E_{gs}=\frac{\alpha }{2}+\frac{1}{8\alpha }$

$$\frac{\partial E}{\partial \alpha }=\frac{1}{2}-\frac{1}{8{\alpha }^2}$$ $$E_{GS}=\frac{\alpha }{2}+\frac{1}{8\alpha }+\frac{\beta }{2}+\frac{1}{8\beta }$$ $$\frac{\partial E}{\partial \alpha }=\frac{1}{2}-\frac{1}{8{\alpha }^2}$$ $$\frac{\partial E}{\partial \beta }=\frac{1}{2}-\frac{1}{8{\beta }^2}$$