Let (x, y) = e xy and r(t) = (t 3 , 1 + t). (a) Calculate and r'(t). (b) Use the Chain Rule

Let ƒ(x, y) = e^xy and r(t) = (t³, 1 + t).

(a) Calculate ∇ƒ and r'(t).
(b) Use the Chain Rule for Paths to calculate d/dt ƒ(r(t)).
(c) Write out the composite ƒ(r(t)) as a function of t and differentiate. Check that the result agrees with part (b).