I. Solve the following problems. 1. Find of -2xy and ax of the function f(x, y) = arccot + In x2+ yz. (8 points) 2. Given that arcsec () + ( x2 - 12)2 = 2. (a) Find dy using implicit differentiation. (6 points) dx dy (b) Find dx using partial differentiation of the function f(x, y) from the given equation. 3. Given that 3e-Art + 2sew - 4wart = 3. aw (a) Find at using implicit differentiation. (6 points) aw (b) Find at using partial differentiation of the function f(r, s, t, w) from the given equati1. Find af and of the function f(x, y) = arccot () + In -2xy ax ay x24 VZ . (8 points) 2. Given that arcsec () + (x2 - y2)z = 2. (a) Find dy dx using implicit differentiation. (6 points) (b) Find dy dx using partial differentiation of the function f(x, y) from the given equation. (6 points) 3. Given that 3e-4rt + 2sew - 4wart = 3. aw (a) Find at using implicit differentiation. (6 points) aw (b) Find at using partial differentiation of the function f(r, s, t, w) from the given equation. (6 points) 4. Use the Chain Rule to find when r = 2, t =-1 of the function f(x, y, z) = e3xyz cos 2xyz ; x=r2 - th , y = th - r, z = r+ t. (8 points) 5. At a certain instant of time, the length of one leg of a right triangle is 10 cm and it is increasing at the rate of 1 cm/min, and the length of the other leg is 12 cm and it is decreasing at the rate of 2 cm/min. Find the rate of change of the acute angle opposite the leg of length 12 cm at the certain instant.side. (6 points)