Find an equation for the plane tangent to the graph ofz= 6 cos(xy) at the point (2,π/6, 3).

i went on to find

partial derivative x = -6 y sin(xy)

partial derivative y = -6 x sin(xy)

then i used the equation for tangent plane

$\displaystyle z=f(a,b)+fx(a,b)(x-a)+fy(a,b)(y-b)$

$\displaystyle z = 6cos(xy) + (-6)ysin(xy)(x-2)+(-6)xsin(xy)(y-\pi/6)$

$\displaystyle z = 6(.5) + (-6)(\frac{\pi}{6})sin(2 * \frac{\pi}{6})(x - 2) + (-6)(2)sin(2 * \frac{\pi}{6})(y - \frac{\pi}{6})$

$\displaystyle z = 3 + (-\pi)*\frac{\sqrt{3}}{2} * (x-2) + (-12)\frac{\sqrt{3}}{2}(y - \frac{\pi}{6})$

The thing is, i have no idea if i did this problem correctly or not. I haven't been taught how to deal with problems like this and trying to learn on my own. Can anyone help? Thanks!