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If (cos x)^y = (cos y)^x, then find dy/dx.

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If (cos x)y = (cos y)x, then find \(\frac{dy}{dx}.\)

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Given,

(cos x)y = (cos y)x

Taking logrithm both sides, we get

log (cos x)y = log (cos y)x

 ⇒ y.log (cos x) = x.log(cos y)

[∵ log mn = n log m]

Differentiating both sides, we get

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