In the next four exercises, form the difference quotients
\frac{f(x + h, y) - f(x, y)}{h} and \frac{f(x, y + h) - f(x, y)}{h} , (h \neq 0).
Then, assuming that x and y are fixed, calculate the limit as h \to 0. What is the connection
between your results and derivatives?
18. f(x, y) = x \sin y.
19. f(x, y) = x^2 e^y.