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Verified answer
Calculus Derivative.x + tan (xy) = 0
dy/dx [x + tan (xy)] = dy/dx 0
1 + sec² (xy) (y + x dy/dx) = 0
1 = -sec² (xy) (y + x dy/dx)
x dy/dx = -1 / sec² (xy) - y
dy/dx = [-1 - y sec² (xy)] / [x sec² (xy)]