Exercise 8

For \(f(x, y) = x^2 \ln y\) at point \(P(3, 1)\) with vector \(u = \langle 1/\sqrt{2}, -1/\sqrt{2} \rangle\): (a) Find the gradient of f. (b) Evaluate the gradient at the point P. (c) Find the rate of change of f at P in the direction of the vector u.