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

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}

\frac{\partial}{\partial y} (x^{- 2} y^{- 3})

\frac{1}{2} x 25 - x^{2}

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

f (x) = \frac{6 x}{x ^{2} + 1}, (1, 3)

\frac{\partial}{\partial y} (\frac{x y ^{2}}{z ^{3}})

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