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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derivative of

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}

\int cos (3 π t) d t

\int 1 - \frac{3}{y} d y

f (x) = - 8 sin (x)

(\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) (y + 9 y^{3})

x \to 3 lim (2 x - 3)

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}