What is the derivative of 1-e^{-e^x} ?

The derivative of 1-e^{-e^x} is e^{x-e^x}

What is the first derivative of 1-e^{-e^x} ?

The first derivative of 1-e^{-e^x} is e^{x-e^x}

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\frac{d}{d x} (1 - e^{- e^{x}})

e^{x - e^{x}}

Solution steps

\frac{d}{d x} (1 - e^{- e^{x}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (1) - \frac{d}{d x} (e^{- e^{x}})

\frac{d}{d x} (1) = 0

\frac{d}{d x} (e^{- e^{x}}) = - e^{- e^{x} + x}

= 0 - (- e^{- e^{x} + x})

Simplify

= e^{x - e^{x}}

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What is the derivative of 1-e^{-e^x} ?
The derivative of 1-e^{-e^x} is e^{x-e^x}
What is the first derivative of 1-e^{-e^x} ?
The first derivative of 1-e^{-e^x} is e^{x-e^x}