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}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

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

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

x \to 0.5 + lim (3 x)

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

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

x \to 1 lim (\frac{1}{( x - 1 ) ^{2}})

\int_{1}^{\infty} e^{x} d x

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}