Determine which of the differentials (or both) is the total differential: a) 2[exp(2x + 2y²) +x] dx + [4y exp(2x + 2y²) + 1] dy; [15 marks] b) 6 sin(y) e²x+ydx + 3(siny+ cosy)e²x+y -2y sin(y²) dy. [15 marks] Find the potential function U(x, y) subject to the condition U(0, 0) = 5 in the case of the total differential. Rubric: 3 marks if the total differential was determined correctly in case (a); 6 marks if the potential function was derived correctly in case (a); 3 4 marks if the constant of integration was found correctly in case (a); 2 marks if the potential function was presented explicitly in the final form in case (a); 3 marks if the total differential was determined correctly in case (b); 6 marks if the potential function was derived correctly in case (b); 4 marks if the constant of integration was found correctly in case (b); 2 marks if the potential function was presented explicitly in the final form in case (b).