What is the derivative of e^{-kx} ?

The derivative of e^{-kx} is -ke^{-kx}

What is the first derivative of e^{-kx} ?

The first derivative of e^{-kx} is -ke^{-kx}

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derivative of

e^{- k x}

- k e^{- k x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

= - k e^{- k x}

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What is the derivative of e^{-kx} ?
The derivative of e^{-kx} is -ke^{-kx}
What is the first derivative of e^{-kx} ?
The first derivative of e^{-kx} is -ke^{-kx}