Solve question with step by step (Calculus and Vector Analysis)

5. (10 points) Given f(.r. y) = CI\" + 41.". answer the following questions: (a) Is f(r.y) differentiable at the point (5. 1)? (b) Determine the equation of the tangent plane at the point (5, l). (c) Determine D..f(5, 1) with v = (4. 5) (d) What is the angle, in radians, between v and V f (5. 1)? 6. (15 points) The path of a particle satises 3: = (QM/3. (t 3)2.si11(t) + 2). r(0) = (5. 4.2) (a) Find the parametrization r[t) of the path. (1)) Find the location of the particle at t'. = 6 (leave your answer in the exact form). (c) \""hat is the velocity of the particle at time t = 0