What is (\partial)/(\partial x)(e^{-ax}) ?

The answer to (\partial)/(\partial x)(e^{-ax}) is -ae^{-ax}

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(\partial)/(\partial x)(e^{-ax})

\frac{\partial}{\partial x} (e^{- a x})

- a e^{- a x}

Solution steps

\frac{\partial}{\partial x} (e^{- a x})

Apply the chain rule:

e^{- a x} \frac{\partial}{\partial x} (- a x)

= e^{- a x} \frac{\partial}{\partial x} (- a x)

\frac{\partial}{\partial x} (- a x) = - a

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

Simplify

= - a e^{- a x}

What is (\partial)/(\partial x)(e^{-ax}) ?
The answer to (\partial)/(\partial x)(e^{-ax}) is -ae^{-ax}