Use difference quotients with $\Delta x = 0.1$ and $\Delta y = 0.1$ to estimate $f_x(1,3)$ and $f_y(1,3)$ where $$f(x,y) = e^{-x}\sin\!\left(y\right).$$

$f_x(1,3) \approx$
$f_y(1,3) \approx$

Then give better estimates by using $\Delta x = 0.01$ and $\Delta y = 0.01$.

$f_x(1,3) \approx$
$f_y(1,3) \approx$