What is the derivative of e^{-x/6} ?

The derivative of e^{-x/6} is -1/6 e^{-x/6}

What is the first derivative of e^{-x/6} ?

The first derivative of e^{-x/6} is -1/6 e^{-x/6}

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\frac{d}{d x} (e^{- \frac{x}{6}})

- \frac{1}{6} e^{- \frac{x}{6}}

Solution steps

\frac{d}{d x} (e^{- \frac{x}{6}})

Apply the chain rule:

e^{- \frac{x}{6}} \frac{d}{d x} (- \frac{x}{6})

= e^{- \frac{x}{6}} \frac{d}{d x} (- \frac{x}{6})

\frac{d}{d x} (- \frac{x}{6}) = - \frac{1}{6}

= e^{- \frac{x}{6}} (- \frac{1}{6})

Simplify

= - \frac{1}{6} e^{- \frac{x}{6}}

y = x^{2} - 5

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

f (x) = 4 x^{2} + 5 x, at x = - 3

\int \frac{4}{- x ^{2} + 6 x + 5} d x

What is the derivative of e^{-x/6} ?
The derivative of e^{-x/6} is -1/6 e^{-x/6}
What is the first derivative of e^{-x/6} ?
The first derivative of e^{-x/6} is -1/6 e^{-x/6}