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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{2} \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) = - 1

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

Simplify

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

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