What is (\partial)/(\partial x)(e^{-x/2}) ?

The answer to (\partial)/(\partial x)(e^{-x/2}) is -1/2 e^{-x/2}

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(\partial)/(\partial x)(e^{-x/2})

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (- \frac{x}{2}) = - \frac{1}{2}

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

Simplify

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

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What is (\partial)/(\partial x)(e^{-x/2}) ?
The answer to (\partial)/(\partial x)(e^{-x/2}) is -1/2 e^{-x/2}