at the point ( \(\displaystyle \frac{\pi}{3} , \frac{\pi}{6} \) )

I keep getting this question wrong, here's my working;

using the product rule on sinxsiny

\(\displaystyle sinx cosy \frac{dy}{dx} + siny cosx = 0 \)

\(\displaystyle \frac{dy}{dx} = -\frac{ siny cosx}{sinx cosy} \)

Is this part correct?