What is the derivative of e^{-1/2 x} ?

The derivative of e^{-1/2 x} is -1/2 e^{-x/2}

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

The first derivative of e^{-1/2 x} is -1/2 e^{-x/2}

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

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

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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