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

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

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

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

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

- e^{- e^{x} + x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

e^{- e^{x}} (- e^{x}) : - e^{- e^{x} + x}

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

\frac{d}{d x} (ln (\frac{( x + 1 ) ( x + 2 )}{x + 3}))

\int_{- 1}^{1} x^{2} d x

\int 4 e^{x + y}

\int cosh (u) d u

y = x^{2} - 5, (- 5, 20)

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