11.6#5

I am also stuck on part 2 of this one

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You're almost right: you just made one little sign error.  You correctly realize that the maximum rate of change is the same as the magnitude of the gradient, and I *think* you correctly realize that the direction of the maximum increase is the unit vector in the direction of the gradient, but it looks like you incorrectly compute that the partial derivative ∂(y/z)/∂z = y/z^2 to get the gradient as
i + j + 5 k instead of the correct ∂(y/z)/∂z = - y/z^2 to get the correct gradient i + j - 5 k