Derivation of P.D.F. from distribution function

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Author computed $F_{X_k} (x)$ as follows. but I don't understand it. Would any member explain me the following computations?

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After studying these author's computations, I understood the differentiation part but I don't understand cancellation part and final term computation.

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I tag this question as 'SOLVED'.  Author's computations are correct. Thank you.

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