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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = e^{x} arctan (x)

2 sin (x) + sin^{2} (x)

\frac{d}{d x} (cot^{3} (x))

\int_{- 2}^{3} \frac{21}{x ^{4}} d x

x \to 3 lim (\frac{9 - x ^{2}}{3 - x})

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