Find the first-order partial derivatives for each of the following:a) z = 4x3 + 2x2y ? 7y5b) z = 2w2 + 8wxy ? x2 + y3c) z = (7x + 3y)3d) z = (x2 + 2y)4e) z = x0.4y0.6f) f(x, y, z) = 10x3y2z42. Find the cross partials for each of the following functions:a) z = x0.3y0.5b) z = w3x4y33. Find the profit-maximising level of (a) output, (b) price, and (c) profit for a monopolist with the demand functions X= 50 - 0.5 Px Y = 76 - Pyand the total cost function c = 3x2 + 2xy + 2y2 + 55.4. Given Q = 4?KL, find (a) MPK and MPL, and (b) determine the effect on Q of a 1-unit change in K and L, where K=50 and L=600.5. Given the equation for the production isoquant25K3/5L2/5 = 5400 find the MRTS, using the implicit function rule.

1. Find the firstorder partial derivatives for each of the following: a) z = 4x3 + 2x33: # 7y5 h] z: 2w2+8wxy x2+y3 c) z = (7x + 3393 d] z = (x2 + 23;)" e) z = 1:043.an f1 mien!) = 10K3Y22' 2. Find the cross partials for each of the following functions: a) z = Xasyas h) z = ng'yg 3. Find the profitmaximising level of (a) output, (b) price, and (c) profit for a monopolist with the demand functions X: 50 0-5 Pa Y : T6 - PF and the total cost function c = 312 + 2):}? + 2312 + 55. 4. Given Q = 4m, find (a) MPK and MP1,, and (1:) determine the effect on Q of a 1unit change in K and L, where K=S and 1:600. 5. Given the equation for the production isoquant zsirs'f'n'tzf5 = 5400 find the MRTS, using the implicit function rule