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Popular >

derivative of 1/(e^{sqrt(x)})

Solution

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

Solution

- \frac{e ^{- x}}{2 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) = - \frac{1}{2 x}

= e^{- x} (- \frac{1}{2 x})

Simplify

e^{- x} (- \frac{1}{2 x}) : - \frac{e ^{- x}}{2 x}

= - \frac{e ^{- x}}{2 x}

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Frequently Asked Questions (FAQ)

What is the derivative of 1/(e^{sqrt(x)}) ?
The derivative of 1/(e^{sqrt(x)}) is -(e^{-sqrt(x)})/(2sqrt(x))
What is the first derivative of 1/(e^{sqrt(x)}) ?
The first derivative of 1/(e^{sqrt(x)}) is -(e^{-sqrt(x)})/(2sqrt(x))