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Let f(x, y) = x^2 ln(x^3 + y). (a) Find the gradient of f. (b) Find...

Let f(x, y) = x^2 ln(x^3 + y).

(a) Find the gradient of f.

(b) Find the direction in which the function decreases most rapidly at the point P(2, 1). (Give the direction as a unit vector.)

(c) Find the directions of zero change of f at the point P(2, 1). (Give both directions as a unit vector.)

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