Rate of change of a gradient with direction in 3D

f(x,y,z)=sqrt(x+y+z)
P=(2,1,1)
u=<2/3, 1/3, 2/3>

How do you find the rate of change of f at P in the direction of the vector u?

You should have this equation already.
 ∇f ⋅ û

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You do need to know u.

| ∇f(P) | is the maximum rate of change at P. That maximum rate of change occurs in the direction of  ∇f(P)

You want to find the rate of change at P, but in the direction of u. This is not necessarily the maximizing direction and its magnitude isnt necessarily the optimum.

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I dont know what you keep posting. Is that  ∇f ⋅ û or something else? Follow the equation.

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Why are you dividing by the magnitude of the gradient vector? Is that a part of the equation or not? You are just tossing in your own stuff. The u vector is supposed to be a unit vector, not the gradient vector.

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Yes. It does. Was that so hard?

I didnt even do the work for you. All I did was tell you to follow the equation they already gave you.