1. (40 points) Find the first derivative (dy/dx) of the following functions: a. y = In (2x3 +1) b. y = e-2x c. y = (x3 + 3) (3x4 - 1 ) + 6x2 d. Vx+ Vy = Va, where a is a constant. (Must use implicit differentiation.) 2. (10 points) Solve for the below 2 equations 2 unknowns: -4y+7z = 11 -2y+5z =7 3. Suppose an indifference curve is written as Uo=100=F2/3$1/3, where F and S represent food and shelter, respectively. Uo is a given utility level fixed at 100. a.(10 points) What is the slope of the indifference curve (dF/dS)? Please simplify your answer. (Must use implicit differentiation to find the slope.)