What is the derivative of e^{(-0.5x}) ?

The derivative of e^{(-0.5x}) is -0.5e^{-0.5x}

What is the first derivative of e^{(-0.5x}) ?

The first derivative of e^{(-0.5x}) is -0.5e^{-0.5x}

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\frac{d}{d x} (e^{(- 0.5 x)})

- 0.5 e^{- 0.5 x}

Solution steps

\frac{d}{d x} (e^{(- 0.5 x)})

Apply the chain rule:

e^{- 0.5 x} \frac{d}{d x} (- 0.5 x)

= e^{- 0.5 x} \frac{d}{d x} (- 0.5 x)

\frac{d}{d x} (- 0.5 x) = - 0.5

= e^{- 0.5 x} (- 0.5)

Simplify

= - 0.5 e^{- 0.5 x}

What is the derivative of e^{(-0.5x}) ?
The derivative of e^{(-0.5x}) is -0.5e^{-0.5x}
What is the first derivative of e^{(-0.5x}) ?
The first derivative of e^{(-0.5x}) is -0.5e^{-0.5x}