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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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t \cdot e^{- \frac{t}{2}}

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