What is the derivative of-27e^{-3x} ?

The derivative of-27e^{-3x} is 81e^{-3x}

What is the first derivative of-27e^{-3x} ?

The first derivative of-27e^{-3x} is 81e^{-3x}

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\frac{d}{d x} (- 27 e^{- 3 x})

81 e^{- 3 x}

Solution steps

\frac{d}{d x} (- 27 e^{- 3 x})

Take the constant out:

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

= - 27 \frac{d}{d x} (e^{- 3 x})

Apply the chain rule:

e^{- 3 x} \frac{d}{d x} (- 3 x)

= e^{- 3 x} \frac{d}{d x} (- 3 x)

\frac{d}{d x} (- 3 x) = - 3

= - 27 e^{- 3 x} (- 3)

Simplify

= 81 e^{- 3 x}

What is the derivative of-27e^{-3x} ?
The derivative of-27e^{-3x} is 81e^{-3x}
What is the first derivative of-27e^{-3x} ?
The first derivative of-27e^{-3x} is 81e^{-3x}