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

The answer to (\partial)/(\partial x)(e^{-x/y}+ln(y/x)) is -(e^{-x/y})/y-1/x

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

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

- \frac{e ^{- \frac{x}{y}}}{y} - \frac{1}{x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

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

\int \frac{7}{x ^{2} + 4} d x

t^{2} y^{^{'}} + y = sin (t)

\frac{d}{d x} (- arcsin (\frac{a ^{2} - x ^{2}}{a}))

y = x^{2}, at x = - \frac{3}{4}

What is (\partial)/(\partial x)(e^{-x/y}+ln(y/x)) ?
The answer to (\partial)/(\partial x)(e^{-x/y}+ln(y/x)) is -(e^{-x/y})/y-1/x