Solution
\(f_x(x,y)\)
\[\begin{align}f(x, y) &= sin(y)cos(x) \\ \\ f_x(x,y) &= -sin(y)sin(x) \\ \\ f_x(\frac{\pi}{3},\frac{\pi}{3}) &= -sin(\frac{\pi}{3})sin(\frac{\pi}{3}) = -\frac{\sqrt{3}}{2}*\frac{\sqrt{3}}{2} = - \frac{3}{4} \end{align}\]
\(f_y(x,y)\)
\[\begin{align}f_y(x,y) &= cos(x)cos(y) \\\\ f_y(\frac{\pi}{3},\frac{\pi}{3}) &= cos(\frac{\pi}{3})cos(\frac{\pi}{3}) = \frac{1}{2}*\frac{1}{2} = \frac{1}{4}\end{align}\]