Chapter 9.1, Problem 31E

To determine

(a)

To find:

The value of $\frac{f\left(x+h,y\right)-f\left(x,y\right)}{h}$.

To determine

(b)

To find:

The value of $\frac{f\left(x,y+h\right)-f\left(x,y\right)}{h}$.

To determine

(c)

To find:

The value of $\underset{h\to 0}{\lim }\frac{f\left(x+h,y\right)-f\left(x,y\right)}{h}$.

To determine

(d)

To find:

The value of $\underset{h\to 0}{\lim }\frac{f\left(x,y+h\right)-f\left(x,y\right)}{h}$.