Suppose f(x, y)=xy, p=(−4,−4) and v=2i+3j. a. find the gradient of f. ∇f= i+ j note: your answers should be expressions of x and y; e. g. "3x - 4y" b. find the gradient of f at the point p. (∇f)(p)= i+ j note: your answers should be numbers c. find the directional derivative of f at p in the direction of v. duf= note: your answer should be a number d. find the maximum rate of change of f at p. note: your answer should be a number e. find the (unit) direction vector in which the maximum rate of change occurs at p. u= i+ j note: your answers should be numbers