2. Show that the following vector field F(x,y) = (yet + sin(y))i + (ex + x cos(y))j is conservative by responding to the following steps: a.) Determine both P(x, y) and Q(x, y) given F. b.) Demonstrate your answers in a. ) satisfy Clairaut's theorem. c.) Partially integrate P with respect to x to obtain the potential f(x,y) = / P(x, y)dr =(x, y) + C(y). where o(r, y) is the anti-derivative of P(a, y) with respect to r and C(y) is a function of y such that ac(y)/Or = 0. d.) Since F is conservative, Of(x, y)/dy = Q(x, y). Use this fact to solve for C(y). e.) Substitute your answer from d.) into your answer for c.) to obtain f such that Vf = F