Let $f(x,y) = e^{-2x}\sin\!\left(4y\right)$.
(a) Using difference quotients with $\Delta x = 0.1$ and $\Delta y = 0.1$, we estimate
$f_x (2, -2) \approx$
$f_y (2, -2) \approx$

(b) Using difference quotients with $\Delta x = 0.01$ and $\Delta y = 0.01$, we find better estimates:
$f_x (2, -2) \approx$
$f_y (2, -2) \approx$