Answer
a. $\frac{\partial z}{\partial x}=12$ or $\frac{\partial z}{\partial x}=-4$
b. $\frac{\partial z}{\partial y}=18$ or $\frac{\partial z}{\partial y}=-4$
c. 12;
d. -40.
Work Step by Step
$f_{x}(x,y) =12x -4y$
$f_{y}(x,y)=-4x +18y$
a. $\frac{\partial z}{\partial x}=f_{xx}(x,y)=12$
$\frac{\partial z}{\partial x}=f_{xy}(x,y)=-4$
b. $\frac{\partial z}{\partial y}=f_{yy}(x,y)=18$
$\frac{\partial z}{\partial y}=f_{yx}(x,y)=-4$
c. Since $\frac{\partial f}{\partial x}=12x - 4y$
$\frac{\partial f}{\partial x}(2,3)=12(2)-4(3)=12$
d. $f_{y}(1,-2)=-4(1)+18(-2)=-40$
