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

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

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

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

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

- 1

Solution steps

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

Simplify

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

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d x}{d x}

Apply the common derivative:

\frac{d x}{d x} = 1

= - 1

\frac{1}{s + 1}

\int \frac{y - 2}{y ( y - 4 ) ( y + 3 )} d y

\frac{( x ^{2} - 4 )}{x}

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

\int \frac{2}{4 + x ^{2}} d x

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