I need to find the extrema of the following function in the range $-2\pi$ and $2\pi$ for both $x$ and $y$, but I don't know how to go about doing it since it's a bit weird and not similar to other functions I've seen:

$$f(x,y)=\frac{\sin (x) \sin (y)}{xy}$$

I've evaluated the gradient function as below:

$\nabla f = <\frac{\sin (y) (x \cos (x)-\sin (x))}{x^2 y}, \frac{\sin (x) (y \cos (y)-\sin (y))}{y^2 x}>$

but setting it to zero gives a few answers for $x$ and $y$, none of which seem to be the right answer.

The following is the sketch of the graph in the aforementioned range. According to WolframAlpha, it should have it's local extrema at $\{0, 4.49\}$, $\{0, -4.49\}$, $\{4.49, 0\}$, $\{-4.49, 0\}$.

[![enter image description here](https://i.stack.imgur.com/d8kPm.png)](https://i.stack.imgur.com/d8kPm.png)