Are My Partial Derivatives Correct for Linearization?

[DeadxBunny]

Original question: Let f(x,y) = ln(xy) + yzcos(xz). Find the linearization of f at the point (1,1,pi/2). Use this linearization to estimate the change in the value of the function resulting from moving from (1, 1, pi/2) to (1.1, 1.2, pi/2 + 0.2).

I believe the first steps to completing this problem are finding the partial derivatives of x, y and z at the point (1, 1, pi/2) which I have done:
fx = 1 – (pi/2)^2
fy = 1
fz = pi/2
Are these correct?

If so, what do I do next?

 

[Tide]

You just need to use this:

$$f(x, y, z) = f(x_0, y_0, z_0) + f_x (x-x_0) + f_y (y-y_0) + f_z (z-z_0) +O(\Delta^2)$$

 

[HallsofIvy]

f_z(1, 1, pi/2)= -pi/2, not pi/2.