Find the equation to the tangent and the normal to the curve $\displaystyle sinx siny = \frac{\sqrt{3}}{4} $

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?