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Find the derivative of e(ex)

Find the derivative of the following function:

    \[ f(x) = e^{\left( e^x \right) }. \]


Again, we use the chain rule and the formula for the derivative of the exponential,

    \[  f'(x) = \left( e^x \right)' \left( e^{\left(e^x\right)} \right) = e^x e^{\left(e^x\right)}\]

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