Find the slope of the tangent line to the curve at the point .
when i do this i get to 6cos(x)-4sin(y)(dy/dx)+6sinxsiny(dy/dx)-cosy6cosx
then i get -7/4
where is my mistake?
I added something that you missed in red.
From there, you should have $\displaystyle 6\cos(3\pi)-4\sin\left(\tfrac{7}{2}\pi\right)\frac{\,dy}{\,dx} +6\sin\left(3\pi\right)\sin\left(\tfrac{7}{2}\pi\r ight)\frac{\,dy}{\,dx}-\cos\left(\tfrac{7}{2}\pi\right)\cos\left(3\pi\rig ht)=-1$ $\displaystyle \implies -6-4\frac{\,dy}{\,dx}=-1\implies -4\frac{\,dy}{\,dx}=5\implies \frac{\,dy}{\,dx}=-\frac{5}{4}$
Does this make sense?