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

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

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

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

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

- \frac{e ^{- \frac{x}{t}}}{t}

Solution steps

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

Treat

t

as a constant

Apply the chain rule:

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

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

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

= e^{- \frac{x}{t}} (- \frac{1}{t})

Simplify

e^{- \frac{x}{t}} (- \frac{1}{t}) : - \frac{e ^{- \frac{x}{t}}}{t}

= - \frac{e ^{- \frac{x}{t}}}{t}

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

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

n = 1 \sum \infty \frac{1}{n} + \frac{1}{n ^{2}}

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

x \to \infty lim (ln (x))

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