What is (\partial)/(\partial x)(1/(e^x)) ?

The answer to (\partial)/(\partial x)(1/(e^x)) is -e^{-x}

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(\partial)/(\partial x)(1/(e^x))

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

- e^{- x}

Solution steps

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

Apply exponent rule:

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

= \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

= e^{- x} (- 1)

Simplify

= - e^{- x}

9 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0

\frac{6}{( 4 x + 1 )}

e^{- x}, 0, 1

What is (\partial)/(\partial x)(1/(e^x)) ?
The answer to (\partial)/(\partial x)(1/(e^x)) is -e^{-x}