What is the derivative derivative of 1/((e^x)) ?

The derivative derivative of 1/((e^x)) is -e^{-x}

What is the first derivative derivative of 1/((e^x)) ?

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

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derivative of

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

- e^{- x}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

= e^{- x} (- 1)

Simplify

= - e^{- x}

\frac{d y}{d x} y = x sin (x)

\frac{1}{( y ^{2} )}

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

f (x) = cos (x)

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

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