(cos x)y = (cos y)x
Taking log on both sides,
y ln(cos x) = x ln(cos y)
Differentiating both sides w.r.t x, we get
dy/dx × ln(cos x) + y × (-sin x)/cos x = ln(cos y) + x × (-sin y)/cos y × dy/dx
∴ dy/dx = ln(cos y) + y tan x
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ln(cos x) + x tan y