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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

sin (\frac{4}{x})

\int x^{2} e^{- 4 x} d x

x = y^{2} + 3, x = y, y = - 1, y = 1

n = 9 \sum \infty \frac{1}{n ( n - 1 )}

x^{2} - 2 x

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