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Gradient and rate of change

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Find the gradient of f
Evaluate the gradient at the point P
Find the rate of change of f at P in the direction of the vector u

f(x,y,z)= xy^2z^3, P(1,-2,1), u=<1/squareroot(3), -1/squareroot(3), 1/squareroot(3)>.

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The solution provides an example of finding gradient and rate of change.