What is (\partial)/(\partial x)(5/(e^x)) ?

The answer to (\partial)/(\partial x)(5/(e^x)) is -5e^{-x}

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(\partial)/(\partial x)(5/(e^x))

\frac{\partial}{\partial x} (\frac{5}{e ^{x}})

- 5 e^{- x}

Solution steps

\frac{\partial}{\partial x} (\frac{5}{e ^{x}})

Take the constant out:

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

= 5 \frac{\partial}{\partial x} (\frac{1}{e ^{x}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 5 \frac{\partial}{\partial x} (e^{- x})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (- x) = - 1

= 5 e^{- x} (- 1)

Simplify

= - 5 e^{- x}

What is (\partial)/(\partial x)(5/(e^x)) ?
The answer to (\partial)/(\partial x)(5/(e^x)) is -5e^{-x}