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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

x \to 0 lim (x^{4} sin (\frac{4}{x}))

\frac{1 + 4 s}{s ( 2 s ^{2} + 2 s + 1 )}

\frac{d}{d x} (\frac{ln ( x )}{1 + x})

y^{^{'}} - 12 x^{11} y = e^{x^{12}}

\frac{d}{d x} (- 18 e^{- 2 x})

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