What is (\partial)/(\partial x)(e^{-9x}) ?

The answer to (\partial)/(\partial x)(e^{-9x}) is -9e^{-9x}

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(\partial)/(\partial x)(e^{-9x})

\frac{\partial}{\partial x} (e^{- 9 x})

- 9 e^{- 9 x}

Solution steps

\frac{\partial}{\partial x} (e^{- 9 x})

Apply the chain rule:

e^{- 9 x} \frac{\partial}{\partial x} (- 9 x)

= e^{- 9 x} \frac{\partial}{\partial x} (- 9 x)

\frac{\partial}{\partial x} (- 9 x) = - 9

= e^{- 9 x} (- 9)

Simplify

= - 9 e^{- 9 x}

What is (\partial)/(\partial x)(e^{-9x}) ?
The answer to (\partial)/(\partial x)(e^{-9x}) is -9e^{-9x}