x² - y² (10 points) Let f(x,y): = (a) (6 points) For each vector u = (1, 2), calculate the directional derivative Duƒ(1,1). (b) (4 points) Determine all unit vectors u for which Duf(1, 1) = 0.

a) Find F‘(0)  for the function f(x)=3xe5x b) Given vectors a=(1,3,-2) and b=(1,1,2) , find  3a +2b     Note: an arrow representing direction should be on the alphabets

The vector describing a particular particle is given by T(t) = Rcos (wt)î + Rsin (wt) ĵ, where R and w are constants. (a) What is the magnitude of the position, |7|? What is its unit vector, f? (b) What is the velocity, ī, of this particle? What is it's magnitude, |0|? What is its unit vector, î? (c) What is the acceleration, a, of this particle? What is it's magnitude, Jā|? What is its unit vector, â? (d) Show that the acceleration points opposite to the position, ř° (i.e., â x -î), and determine the proportionality constant. |

Find the maximum rate of change of f(x, y) Maximum rate of change: 2/5 In(x? + y?) at the point (-4, -3) and the direction in which it occurs. Direction (unit vector) in which it occurs: -8/25 -6/25 出)