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

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

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

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

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

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

Solution steps

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

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