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

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

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

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

- \frac{e ^{- \frac{x}{y}}}{y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= e^{- \frac{x}{y}} (- \frac{1}{y})

Simplify

e^{- \frac{x}{y}} (- \frac{1}{y}) : - \frac{e ^{- \frac{x}{y}}}{y}

= - \frac{e ^{- \frac{x}{y}}}{y}

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