Final answer:
The equation of the tangent plane is z = -2x - 2y - 2.
Step-by-step explanation:
To find the equation of the tangent plane to the given surface at the specified point, we need to find the partial derivatives of the surface equation with respect to x and y. The equation of a plane is given by z = Ax + By + C, where A, B, and C are constants.
First, we find the partial derivative of z with respect to x, which is -y*sin(x-y). Then, we find the partial derivative of z with respect to y, which is cos(x-y)-y*sin(x-y). Plugging in the coordinates of the specified point (-2, -2, -2) into these derivatives gives us the values for A, B, and C.
Therefore, the equation of the tangent plane to the given surface at the point (-2, -2, -2) is z = (-2)*x + (-2)*y - 2.