Question

Find dy/dx by implicit differentiation for ycos(x)=xcos(y)

Answer 1

dy/dx = (cos y + y sin x) / (cos x + x sin y)

Explanation:

y cos x = x cos y

y (-sin x) + dy/dx cos x = x (-sin y dy/dx) + cos y

-y sin x + dy/dx cos x = -x sin y dy/dx + cos y

dy/dx (cos x + x sin y) = cos y + y sin x

dy/dx = (cos y + y sin x) / (cos x + x sin y)