What is (\partial)/(\partial x)(e^{-x/(2y)}) ?

The answer to (\partial)/(\partial x)(e^{-x/(2y)}) is -(e^{-x/(2y)})/(2y)

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(\partial)/(\partial x)(e^{-x/(2y)})

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

- \frac{e ^{- \frac{x}{2 y}}}{2 y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (- \frac{x}{2 y}) = - \frac{1}{2 y}

= e^{- \frac{x}{2 y}} (- \frac{1}{2 y})

Simplify

e^{- \frac{x}{2 y}} (- \frac{1}{2 y}) : - \frac{e ^{- \frac{x}{2 y}}}{2 y}

= - \frac{e ^{- \frac{x}{2 y}}}{2 y}

x \to 0 lim (\frac{4}{14 + x})

y = \frac{( x - 2 )}{y + 3}

f (x) = e^{x^{2} + 1}

x \to 0 lim (1 + \frac{1}{4 x ^{2}})

\int \frac{x - 2}{( x + 1 )} d x

What is (\partial)/(\partial x)(e^{-x/(2y)}) ?
The answer to (\partial)/(\partial x)(e^{-x/(2y)}) is -(e^{-x/(2y)})/(2y)