Find all the first and second order partial derivatives of f

Solution

Holding y constant: f_x = - 3cos(x-y) +6 sin(2x+y) Holding x constant: f_y = -3 cos(x-y) + 6 sin(2x+y) * -1 = -3 cos(x-y) - 12 sin(2x+y). ------------------- Onto the second derivatives. f_xx = (?/?x) [-6 cos(2x+y) - 8 sin(x-y)] = 12 sin(2x+y) - 8 cos(x-y) f_xy = f_yx = (?/?y) [-6 cos(2x+y) - 8 sin(x-y)] = 6 sin(2x+y) + 8 cos(x-y) f_yy = (?/?y) [-3 cos(2x+y) + 8 sin(x-y)] = 3 sin(2x+y) - 8 cos(x-y).