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Answer 1

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Answer 2

$y = log_{e}( {e}^{x} ( { \frac{x - 2}{x + 2} )}^{ \frac{3}{4} } ) \\ y = x + \frac{3}{4} ln((x - 2)) - \frac{3}{4} ln(x + 2) \\ \frac{dy}{dx} = 1 + \frac{3}{4} ( \frac{1}{x - 2} - \frac{1}{x + 2} ) \\ \frac{dy}{dx} = 1 + \frac{3}{4} ( \frac{x + 2 - x + 2}{ {x}^{2} - 4 } ) \\ \frac{dy}{dx} = 1 + \frac{3}{ {x}^{2} - 4 } \\ \frac{dy}{dx} = \frac{ {x }^{2} - 4 + 3 }{ {x }^{2} - 4 } = \frac{ {x}^{2} - 1 }{ {x}^{2} - 4}$

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