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Find the derivative of e1/x

Find the derivative of the function:

    \[ f(x) = e^{\frac{1}{x}}. \]


Using the formula for the derivative of the exponential and the chain rule we compute,

    \[ f'(x) = \left( \frac{-1}{x^2} \right) e^{\frac{1}{x}} = -\frac{e^{\frac{1}{x}}}{x^2}. \]

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