Find the equation of the tangent plane to the surface z=cos(9x)cos(4y) at the point (−pi/2,−3pi/2,0)

Find the equation of the tangent plane to the surface z=cos(9x)cos(4y) at the point (−pi/2,−3pi/2,0)

Taking partial derivatives,
z_x = -9 sin(9x) cos(4y), and z_y = -4 cos(9x) sin(4y).

So, z_x (-π/2, -3π/2) = 9 , and z_y (-π/2, -3π/2) = 0

Hence, the equation of the tangent plane is
z - 0 = 9(x - (-π/2)) + 0(y - (-3π/2)).

I hope this helps!