Are My Partial Derivatives Correct for Linearization?

AI Thread Summary
The discussion centers on finding the linearization of the function f(x,y,z) = ln(xy) + yzcos(xz) at the point (1,1,pi/2) and estimating the function's change when moving to (1.1, 1.2, pi/2 + 0.2). The user calculates the partial derivatives at the specified point, initially obtaining fx = 1 - (pi/2)^2, fy = 1, and fz = pi/2. However, it is pointed out that fz should actually be -pi/2 instead of pi/2. The next step involves applying the linearization formula to estimate the change in the function's value.
DeadxBunny
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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?
 
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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)
 
fz(1, 1, pi/2)= -pi/2, not pi/2.
 
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