Evaluate \(f_x(x,y)\) and \(f_y(x,y)\) at the indicated point.
The question: \[f(x,y) = \frac{4}{xy}\]
With respect to \(x\)
\[ \frac{d}{dx} \Big( \frac{4}{xy} \Big)\\ = \frac{4(\frac{d}{dx}(\frac{1}{x}))}{y}\\ =\Big( \frac{-1}{x^2} \Big) \Big( \frac{4}{y} \Big) \]
With respect to \(y\)
\[ \frac{d}{dy} \Big( \frac{4}{xy} \Big)\\ = \frac{4(\frac{d}{dx}(\frac{1}{y}))}{y}\\ =\Big( \frac{-1}{y^2} \Big) \Big( \frac{4}{x} \Big) \]