Chapter 9.2, Problem 2E

To determine

a.

To find:

The value of $\frac{\partial z}{\partial x}$ for the function $z=g\left(x,y\right)=8x+6x^{2}y+2y^2$ by using the formal definition of the partial derivative.

To determine

b.

To find:

The value of $\frac{\partial z}{\partial y}$ for the function $z=g\left(x,y\right)=8x+6x^{2}y+2y^2$ by using the formal definition of the partial derivative.

To determine

c.

To find:

The value of $\frac{\partial g}{\partial x}\left(-3,0\right)$ for the function $z=g\left(x,y\right)=8x+6x^{2}y+2y^2$ by using the formal definition of the partial derivative.

To determine

d.

To find:

The value of $f_y\left(1,-2\right)$ for the function $z=g\left(x,y\right)=8x+6x^{2}y+2y^2$ by using the formal definition of the partial derivative.