A complex differentiation ?

Calculus Level pending

What is the differentiation of y with respect to x if \(y=ln e^{n(\pi)i}\) where n is a natural number? If the answer can be represented as \(\frac{p}{q}\).Then find the derivative of \(p+q\) Hint:\(ln\) is the natural log which is equal to \(log_{e}\)

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