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Problem 4. Find the first partial derivatives (i.e. fr and fy ) of the following functions. A) f(x, y) = Vxly B) f(x, y, z) = 13 cos (y + 22) Problem 5. Find all second partial derivatives of the following functions. Does fry = fyx ? A) f(x, y) = my by' + 2x y B) f(x, y) = rty az az Problem 6. Use implicit differentiation to find ax and ay for yz + x lny = 22. Problem 7. Determine if the function u(x, y) = x' +2xy ty is "harmonic, " i.e. a solution to the Laplace equation usr + Uyy = 0