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

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

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

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

e^{- x}

Solution steps

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

Take the constant out:

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

= - \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}

\frac{x ^{2} - 9 x + 8}{x ^{2} + 9}

n = 1 \sum \infty \frac{8}{n} - \frac{8}{n + 1}

\int \frac{6 x - 11}{( x - 1 ) ^{2}} d x

\frac{6}{( 6 - x ^{6} ) ^{\frac{3}{2}}}

\int \frac{x ^{3}}{( x ^{2} + 4 ) ^{\frac{3}{2}}} d x

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