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

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

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

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

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derivative of

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

e^{- 2 x}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= e^{- 2 x}

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